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Sie erfüllt die quadrierte Gleichung, aber nicht die Ausgangsgleichung, weil eine Wurzel nie negativ ist.",[564,1075,1076,1077,1127],{},"Außerdem muss der Radikand ",[607,1078,1080,1104],{"className":1079},[610],[607,1081,1083],{"className":1082},[614],[616,1084,1085],{"xmlns":618},[620,1086,1087,1101],{},[623,1088,1089,1091,1095,1098],{},[629,1090,631],{},[633,1092,1094],{"stretchy":1093},"false","(",[629,1096,1097],{},"x",[633,1099,1100],{"stretchy":1093},")",[640,1102,1103],{"encoding":642},"T(x)",[607,1105,1107],{"className":1106,"ariaHidden":648},[647],[607,1108,1110,1113,1116,1120,1123],{"className":1109},[652],[607,1111],{"className":1112,"style":1031},[656],[607,1114,631],{"className":1115,"style":695},[661,694],[607,1117,1094],{"className":1118},[1119],"mopen",[607,1121,1097],{"className":1122},[661,694],[607,1124,1100],{"className":1125},[1126],"mclose"," nicht negativ sein, sonst ist die Wurzel nicht definiert.",[559,1129,1131],{"id":1130},"beispiele","Beispiele",[564,1133,1134],{},"Einfacher Fall:",[607,1136,1139],{"className":1137},[1138],"katex-display",[607,1140,1142,1209],{"className":1141},[610],[607,1143,1145],{"className":1144},[614],[616,1146,1148],{"xmlns":618,"display":1147},"block",[620,1149,1150,1206],{},[623,1151,1152,1166,1168,1171,1175,1178,1180,1182,1184,1186,1188,1190,1193,1195,1197,1199,1201,1203],{},[626,1153,1154],{},[623,1155,1156,1158,1160,1163],{},[779,1157,781],{},[629,1159,1097],{},[633,1161,1162],{},"−",[779,1164,1165],{},"1",[633,1167,635],{},[779,1169,1170],{},"3",[1172,1173,1174],"mtext",{},"  ",[633,1176,1177],{},"⇒",[1172,1179,1174],{},[779,1181,781],{},[629,1183,1097],{},[633,1185,1162],{},[779,1187,1165],{},[633,1189,635],{},[779,1191,1192],{},"9",[1172,1194,1174],{},[633,1196,1177],{},[1172,1198,1174],{},[629,1200,1097],{},[633,1202,635],{},[779,1204,1205],{},"5",[640,1207,1208],{"encoding":642},"\\sqrt{2x - 1} = 3 \\;\\Rightarrow\\; 2x - 1 = 9 \\;\\Rightarrow\\; x = 5",[607,1210,1212,1295,1320,1342,1360,1384,1403],{"className":1211,"ariaHidden":648},[647],[607,1213,1215,1219,1286,1289,1292],{"className":1214},[652],[607,1216],{"className":1217,"style":1218},[656],"height:1.04em;vertical-align:-0.1256em;",[607,1220,1222],{"className":1221},[661,662],[607,1223,1225,1277],{"className":1224},[666,667],[607,1226,1228,1274],{"className":1227},[671],[607,1229,1232,1261],{"className":1230,"style":1231},[675],"height:0.9144em;",[607,1233,1235,1238],{"className":1234,"style":681},[680],[607,1236],{"className":1237,"style":686},[685],[607,1239,1241,1244,1247,1251,1255,1258],{"className":1240,"style":690},[661],[607,1242,781],{"className":1243},[661],[607,1245,1097],{"className":1246},[661,694],[607,1248],{"className":1249,"style":1250},[736],"margin-right:0.2222em;",[607,1252,1162],{"className":1253},[1254],"mbin",[607,1256],{"className":1257,"style":1250},[736],[607,1259,1165],{"className":1260},[661],[607,1262,1264,1267],{"style":1263},"top:-2.8744em;",[607,1265],{"className":1266,"style":686},[685],[607,1268,1270],{"className":1269,"style":706},[705],[708,1271,1272],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,1273],{"d":718},[607,1275,723],{"className":1276},[722],[607,1278,1280],{"className":1279},[671],[607,1281,1284],{"className":1282,"style":1283},[675],"height:0.1256em;",[607,1285],{},[607,1287],{"className":1288,"style":737},[736],[607,1290,635],{"className":1291},[741],[607,1293],{"className":1294,"style":737},[736],[607,1296,1298,1302,1305,1308,1311,1314,1317],{"className":1297},[652],[607,1299],{"className":1300,"style":1301},[656],"height:0.6444em;",[607,1303,1170],{"className":1304},[661],[607,1306],{"className":1307,"style":737},[736],[607,1309],{"className":1310,"style":737},[736],[607,1312,1177],{"className":1313},[741],[607,1315],{"className":1316,"style":737},[736],[607,1318],{"className":1319,"style":737},[736],[607,1321,1323,1327,1330,1333,1336,1339],{"className":1322},[652],[607,1324],{"className":1325,"style":1326},[656],"height:0.7278em;vertical-align:-0.0833em;",[607,1328,781],{"className":1329},[661],[607,1331,1097],{"className":1332},[661,694],[607,1334],{"className":1335,"style":1250},[736],[607,1337,1162],{"className":1338},[1254],[607,1340],{"className":1341,"style":1250},[736],[607,1343,1345,1348,1351,1354,1357],{"className":1344},[652],[607,1346],{"className":1347,"style":1301},[656],[607,1349,1165],{"className":1350},[661],[607,1352],{"className":1353,"style":737},[736],[607,1355,635],{"className":1356},[741],[607,1358],{"className":1359,"style":737},[736],[607,1361,1363,1366,1369,1372,1375,1378,1381],{"className":1362},[652],[607,1364],{"className":1365,"style":1301},[656],[607,1367,1192],{"className":1368},[661],[607,1370],{"className":1371,"style":737},[736],[607,1373],{"className":1374,"style":737},[736],[607,1376,1177],{"className":1377},[741],[607,1379],{"className":1380,"style":737},[736],[607,1382],{"className":1383,"style":737},[736],[607,1385,1387,1391,1394,1397,1400],{"className":1386},[652],[607,1388],{"className":1389,"style":1390},[656],"height:0.4306em;",[607,1392,1097],{"className":1393},[661,694],[607,1395],{"className":1396,"style":737},[736],[607,1398,635],{"className":1399},[741],[607,1401],{"className":1402,"style":737},[736],[607,1404,1406,1409],{"className":1405},[652],[607,1407],{"className":1408,"style":1301},[656],[607,1410,1205],{"className":1411},[661],[564,1413,1414,1415,1623,1624,602],{},"Probe: ",[607,1416,1418,1455],{"className":1417},[610],[607,1419,1421],{"className":1420},[614],[616,1422,1423],{"xmlns":618},[620,1424,1425,1452],{},[623,1426,1427,1442,1444,1448,1450],{},[626,1428,1429],{},[623,1430,1431,1433,1436,1438,1440],{},[779,1432,781],{},[633,1434,1435],{},"⋅",[779,1437,1205],{},[633,1439,1162],{},[779,1441,1165],{},[633,1443,635],{},[626,1445,1446],{},[779,1447,1192],{},[633,1449,635],{},[779,1451,1170],{},[640,1453,1454],{"encoding":642},"\\sqrt{2 \\cdot 5 - 1} = \\sqrt{9} = 3",[607,1456,1458,1548,1614],{"className":1457,"ariaHidden":648},[647],[607,1459,1461,1465,1539,1542,1545],{"className":1460},[652],[607,1462],{"className":1463,"style":1464},[656],"height:1.04em;vertical-align:-0.1744em;",[607,1466,1468],{"className":1467},[661,662],[607,1469,1471,1530],{"className":1470},[666,667],[607,1472,1474,1527],{"className":1473},[671],[607,1475,1478,1514],{"className":1476,"style":1477},[675],"height:0.8656em;",[607,1479,1481,1484],{"className":1480,"style":681},[680],[607,1482],{"className":1483,"style":686},[685],[607,1485,1487,1490,1493,1496,1499,1502,1505,1508,1511],{"className":1486,"style":690},[661],[607,1488,781],{"className":1489},[661],[607,1491],{"className":1492,"style":1250},[736],[607,1494,1435],{"className":1495},[1254],[607,1497],{"className":1498,"style":1250},[736],[607,1500,1205],{"className":1501},[661],[607,1503],{"className":1504,"style":1250},[736],[607,1506,1162],{"className":1507},[1254],[607,1509],{"className":1510,"style":1250},[736],[607,1512,1165],{"className":1513},[661],[607,1515,1517,1520],{"style":1516},"top:-2.8256em;",[607,1518],{"className":1519,"style":686},[685],[607,1521,1523],{"className":1522,"style":706},[705],[708,1524,1525],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,1526],{"d":718},[607,1528,723],{"className":1529},[722],[607,1531,1533],{"className":1532},[671],[607,1534,1537],{"className":1535,"style":1536},[675],"height:0.1744em;",[607,1538],{},[607,1540],{"className":1541,"style":737},[736],[607,1543,635],{"className":1544},[741],[607,1546],{"className":1547,"style":737},[736],[607,1549,1551,1555,1605,1608,1611],{"className":1550},[652],[607,1552],{"className":1553,"style":1554},[656],"height:1.04em;vertical-align:-0.1328em;",[607,1556,1558],{"className":1557},[661,662],[607,1559,1561,1596],{"className":1560},[666,667],[607,1562,1564,1593],{"className":1563},[671],[607,1565,1568,1580],{"className":1566,"style":1567},[675],"height:0.9072em;",[607,1569,1571,1574],{"className":1570,"style":681},[680],[607,1572],{"className":1573,"style":686},[685],[607,1575,1577],{"className":1576,"style":690},[661],[607,1578,1192],{"className":1579},[661],[607,1581,1583,1586],{"style":1582},"top:-2.8672em;",[607,1584],{"className":1585,"style":686},[685],[607,1587,1589],{"className":1588,"style":706},[705],[708,1590,1591],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,1592],{"d":718},[607,1594,723],{"className":1595},[722],[607,1597,1599],{"className":1598},[671],[607,1600,1603],{"className":1601,"style":1602},[675],"height:0.1328em;",[607,1604],{},[607,1606],{"className":1607,"style":737},[736],[607,1609,635],{"className":1610},[741],[607,1612],{"className":1613,"style":737},[736],[607,1615,1617,1620],{"className":1616},[652],[607,1618],{"className":1619,"style":1301},[656],[607,1621,1170],{"className":1622},[661],". Also ",[607,1625,1627,1653],{"className":1626},[610],[607,1628,1630],{"className":1629},[614],[616,1631,1632],{"xmlns":618},[620,1633,1634,1650],{},[623,1635,1636,1640,1642,1645,1647],{},[629,1637,1639],{"mathvariant":1638},"double-struck","L",[633,1641,635],{},[633,1643,1644],{"stretchy":1093},"{",[779,1646,1205],{},[633,1648,1649],{"stretchy":1093},"}",[640,1651,1652],{"encoding":642},"\\mathbb{L} = \\{5\\}",[607,1654,1656,1676],{"className":1655,"ariaHidden":648},[647],[607,1657,1659,1663,1667,1670,1673],{"className":1658},[652],[607,1660],{"className":1661,"style":1662},[656],"height:0.6889em;",[607,1664,1639],{"className":1665},[661,1666],"mathbb",[607,1668],{"className":1669,"style":737},[736],[607,1671,635],{"className":1672},[741],[607,1674],{"className":1675,"style":737},[736],[607,1677,1679,1682,1685,1688],{"className":1678},[652],[607,1680],{"className":1681,"style":1031},[656],[607,1683,1644],{"className":1684},[1119],[607,1686,1205],{"className":1687},[661],[607,1689,1649],{"className":1690},[1126],[564,1692,1693],{},"Mit Scheinlösung:",[607,1695,1697],{"className":1696},[1138],[607,1698,1700,1788],{"className":1699},[610],[607,1701,1703],{"className":1702},[614],[616,1704,1705],{"xmlns":618,"display":1147},[620,1706,1707,1785],{},[623,1708,1709,1721,1723,1725,1727,1729,1731,1733,1735,1737,1739,1741,1743,1749,1751,1753,1755,1757,1759,1761,1763,1765,1771,1773,1775,1777,1780,1782],{},[626,1710,1711],{},[623,1712,1713,1715,1718],{},[629,1714,1097],{},[633,1716,1717],{},"+",[779,1719,1720],{},"7",[633,1722,635],{},[629,1724,1097],{},[633,1726,1717],{},[779,1728,1165],{},[1172,1730,1174],{},[633,1732,1177],{},[1172,1734,1174],{},[629,1736,1097],{},[633,1738,1717],{},[779,1740,1720],{},[633,1742,635],{},[774,1744,1745,1747],{},[629,1746,1097],{},[779,1748,781],{},[633,1750,1717],{},[779,1752,781],{},[629,1754,1097],{},[633,1756,1717],{},[779,1758,1165],{},[1172,1760,1174],{},[633,1762,1177],{},[1172,1764,1174],{},[774,1766,1767,1769],{},[629,1768,1097],{},[779,1770,781],{},[633,1772,1717],{},[629,1774,1097],{},[633,1776,1162],{},[779,1778,1779],{},"6",[633,1781,635],{},[779,1783,1784],{},"0",[640,1786,1787],{"encoding":642},"\\sqrt{x + 7} = x + 1 \\;\\Rightarrow\\; x + 7 = x^2 + 2x + 1 \\;\\Rightarrow\\; x^2 + x - 6 = 0",[607,1789,1791,1865,1884,1908,1926,1944,1991,2012,2036,2080,2098,2116],{"className":1790,"ariaHidden":648},[647],[607,1792,1794,1797,1856,1859,1862],{"className":1793},[652],[607,1795],{"className":1796,"style":1218},[656],[607,1798,1800],{"className":1799},[661,662],[607,1801,1803,1848],{"className":1802},[666,667],[607,1804,1806,1845],{"className":1805},[671],[607,1807,1809,1833],{"className":1808,"style":1231},[675],[607,1810,1812,1815],{"className":1811,"style":681},[680],[607,1813],{"className":1814,"style":686},[685],[607,1816,1818,1821,1824,1827,1830],{"className":1817,"style":690},[661],[607,1819,1097],{"className":1820},[661,694],[607,1822],{"className":1823,"style":1250},[736],[607,1825,1717],{"className":1826},[1254],[607,1828],{"className":1829,"style":1250},[736],[607,1831,1720],{"className":1832},[661],[607,1834,1835,1838],{"style":1263},[607,1836],{"className":1837,"style":686},[685],[607,1839,1841],{"className":1840,"style":706},[705],[708,1842,1843],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,1844],{"d":718},[607,1846,723],{"className":1847},[722],[607,1849,1851],{"className":1850},[671],[607,1852,1854],{"className":1853,"style":1283},[675],[607,1855],{},[607,1857],{"className":1858,"style":737},[736],[607,1860,635],{"className":1861},[741],[607,1863],{"className":1864,"style":737},[736],[607,1866,1868,1872,1875,1878,1881],{"className":1867},[652],[607,1869],{"className":1870,"style":1871},[656],"height:0.6667em;vertical-align:-0.0833em;",[607,1873,1097],{"className":1874},[661,694],[607,1876],{"className":1877,"style":1250},[736],[607,1879,1717],{"className":1880},[1254],[607,1882],{"className":1883,"style":1250},[736],[607,1885,1887,1890,1893,1896,1899,1902,1905],{"className":1886},[652],[607,1888],{"className":1889,"style":1301},[656],[607,1891,1165],{"className":1892},[661],[607,1894],{"className":1895,"style":737},[736],[607,1897],{"className":1898,"style":737},[736],[607,1900,1177],{"className":1901},[741],[607,1903],{"className":1904,"style":737},[736],[607,1906],{"className":1907,"style":737},[736],[607,1909,1911,1914,1917,1920,1923],{"className":1910},[652],[607,1912],{"className":1913,"style":1871},[656],[607,1915,1097],{"className":1916},[661,694],[607,1918],{"className":1919,"style":1250},[736],[607,1921,1717],{"className":1922},[1254],[607,1924],{"className":1925,"style":1250},[736],[607,1927,1929,1932,1935,1938,1941],{"className":1928},[652],[607,1930],{"className":1931,"style":1301},[656],[607,1933,1720],{"className":1934},[661],[607,1936],{"className":1937,"style":737},[736],[607,1939,635],{"className":1940},[741],[607,1942],{"className":1943,"style":737},[736],[607,1945,1947,1951,1982,1985,1988],{"className":1946},[652],[607,1948],{"className":1949,"style":1950},[656],"height:0.9474em;vertical-align:-0.0833em;",[607,1952,1954,1957],{"className":1953},[661],[607,1955,1097],{"className":1956},[661,694],[607,1958,1960],{"className":1959},[822],[607,1961,1963],{"className":1962},[666],[607,1964,1966],{"className":1965},[671],[607,1967,1970],{"className":1968,"style":1969},[675],"height:0.8641em;",[607,1971,1973,1976],{"style":1972},"top:-3.113em;margin-right:0.05em;",[607,1974],{"className":1975,"style":838},[685],[607,1977,1979],{"className":1978},[842,843,844,845],[607,1980,781],{"className":1981},[661,845],[607,1983],{"className":1984,"style":1250},[736],[607,1986,1717],{"className":1987},[1254],[607,1989],{"className":1990,"style":1250},[736],[607,1992,1994,1997,2000,2003,2006,2009],{"className":1993},[652],[607,1995],{"className":1996,"style":1326},[656],[607,1998,781],{"className":1999},[661],[607,2001,1097],{"className":2002},[661,694],[607,2004],{"className":2005,"style":1250},[736],[607,2007,1717],{"className":2008},[1254],[607,2010],{"className":2011,"style":1250},[736],[607,2013,2015,2018,2021,2024,2027,2030,2033],{"className":2014},[652],[607,2016],{"className":2017,"style":1301},[656],[607,2019,1165],{"className":2020},[661],[607,2022],{"className":2023,"style":737},[736],[607,2025],{"className":2026,"style":737},[736],[607,2028,1177],{"className":2029},[741],[607,2031],{"className":2032,"style":737},[736],[607,2034],{"className":2035,"style":737},[736],[607,2037,2039,2042,2071,2074,2077],{"className":2038},[652],[607,2040],{"className":2041,"style":1950},[656],[607,2043,2045,2048],{"className":2044},[661],[607,2046,1097],{"className":2047},[661,694],[607,2049,2051],{"className":2050},[822],[607,2052,2054],{"className":2053},[666],[607,2055,2057],{"className":2056},[671],[607,2058,2060],{"className":2059,"style":1969},[675],[607,2061,2062,2065],{"style":1972},[607,2063],{"className":2064,"style":838},[685],[607,2066,2068],{"className":2067},[842,843,844,845],[607,2069,781],{"className":2070},[661,845],[607,2072],{"className":2073,"style":1250},[736],[607,2075,1717],{"className":2076},[1254],[607,2078],{"className":2079,"style":1250},[736],[607,2081,2083,2086,2089,2092,2095],{"className":2082},[652],[607,2084],{"className":2085,"style":1871},[656],[607,2087,1097],{"className":2088},[661,694],[607,2090],{"className":2091,"style":1250},[736],[607,2093,1162],{"className":2094},[1254],[607,2096],{"className":2097,"style":1250},[736],[607,2099,2101,2104,2107,2110,2113],{"className":2100},[652],[607,2102],{"className":2103,"style":1301},[656],[607,2105,1779],{"className":2106},[661],[607,2108],{"className":2109,"style":737},[736],[607,2111,635],{"className":2112},[741],[607,2114],{"className":2115,"style":737},[736],[607,2117,2119,2122],{"className":2118},[652],[607,2120],{"className":2121,"style":1301},[656],[607,2123,1784],{"className":2124},[661],[564,2126,2127,2128,2179,2180,2236],{},"Die quadratische Gleichung hat die Lösungen ",[607,2129,2131,2149],{"className":2130},[610],[607,2132,2134],{"className":2133},[614],[616,2135,2136],{"xmlns":618},[620,2137,2138,2146],{},[623,2139,2140,2142,2144],{},[629,2141,1097],{},[633,2143,635],{},[779,2145,781],{},[640,2147,2148],{"encoding":642},"x = 2",[607,2150,2152,2170],{"className":2151,"ariaHidden":648},[647],[607,2153,2155,2158,2161,2164,2167],{"className":2154},[652],[607,2156],{"className":2157,"style":1390},[656],[607,2159,1097],{"className":2160},[661,694],[607,2162],{"className":2163,"style":737},[736],[607,2165,635],{"className":2166},[741],[607,2168],{"className":2169,"style":737},[736],[607,2171,2173,2176],{"className":2172},[652],[607,2174],{"className":2175,"style":1301},[656],[607,2177,781],{"className":2178},[661]," und 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Probe:",[2238,2239,2240,2464],"ul",{},[576,2241,2242,2292,2293,2179,2390,2463],{},[607,2243,2245,2262],{"className":2244},[610],[607,2246,2248],{"className":2247},[614],[616,2249,2250],{"xmlns":618},[620,2251,2252,2260],{},[623,2253,2254,2256,2258],{},[629,2255,1097],{},[633,2257,635],{},[779,2259,781],{},[640,2261,2148],{"encoding":642},[607,2263,2265,2283],{"className":2264,"ariaHidden":648},[647],[607,2266,2268,2271,2274,2277,2280],{"className":2267},[652],[607,2269],{"className":2270,"style":1390},[656],[607,2272,1097],{"className":2273},[661,694],[607,2275],{"className":2276,"style":737},[736],[607,2278,635],{"className":2279},[741],[607,2281],{"className":2282,"style":737},[736],[607,2284,2286,2289],{"className":2285},[652],[607,2287],{"className":2288,"style":1301},[656],[607,2290,781],{"className":2291},[661],": ",[607,2294,2296,2316],{"className":2295},[610],[607,2297,2299],{"className":2298},[614],[616,2300,2301],{"xmlns":618},[620,2302,2303,2313],{},[623,2304,2305,2309,2311],{},[626,2306,2307],{},[779,2308,1192],{},[633,2310,635],{},[779,2312,1170],{},[640,2314,2315],{"encoding":642},"\\sqrt{9} = 3",[607,2317,2319,2381],{"className":2318,"ariaHidden":648},[647],[607,2320,2322,2325,2372,2375,2378],{"className":2321},[652],[607,2323],{"className":2324,"style":1554},[656],[607,2326,2328],{"className":2327},[661,662],[607,2329,2331,2364],{"className":2330},[666,667],[607,2332,2334,2361],{"className":2333},[671],[607,2335,2337,2349],{"className":2336,"style":1567},[675],[607,2338,2340,2343],{"className":2339,"style":681},[680],[607,2341],{"className":2342,"style":686},[685],[607,2344,2346],{"className":2345,"style":690},[661],[607,2347,1192],{"className":2348},[661],[607,2350,2351,2354],{"style":1582},[607,2352],{"className":2353,"style":686},[685],[607,2355,2357],{"className":2356,"style":706},[705],[708,2358,2359],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,2360],{"d":718},[607,2362,723],{"className":2363},[722],[607,2365,2367],{"className":2366},[671],[607,2368,2370],{"className":2369,"style":1602},[675],[607,2371],{},[607,2373],{"className":2374,"style":737},[736],[607,2376,635],{"className":2377},[741],[607,2379],{"className":2380,"style":737},[736],[607,2382,2384,2387],{"className":2383},[652],[607,2385],{"className":2386,"style":1301},[656],[607,2388,1170],{"className":2389},[661],[607,2391,2393,2415],{"className":2392},[610],[607,2394,2396],{"className":2395},[614],[616,2397,2398],{"xmlns":618},[620,2399,2400,2412],{},[623,2401,2402,2404,2406,2408,2410],{},[779,2403,781],{},[633,2405,1717],{},[779,2407,1165],{},[633,2409,635],{},[779,2411,1170],{},[640,2413,2414],{"encoding":642},"2 + 1 = 3",[607,2416,2418,2436,2454],{"className":2417,"ariaHidden":648},[647],[607,2419,2421,2424,2427,2430,2433],{"className":2420},[652],[607,2422],{"className":2423,"style":1326},[656],[607,2425,781],{"className":2426},[661],[607,2428],{"className":2429,"style":1250},[736],[607,2431,1717],{"className":2432},[1254],[607,2434],{"className":2435,"style":1250},[736],[607,2437,2439,2442,2445,2448,2451],{"className":2438},[652],[607,2440],{"className":2441,"style":1301},[656],[607,2443,1165],{"className":2444},[661],[607,2446],{"className":2447,"style":737},[736],[607,2449,635],{"className":2450},[741],[607,2452],{"className":2453,"style":737},[736],[607,2455,2457,2460],{"className":2456},[652],[607,2458],{"className":2459,"style":1301},[656],[607,2461,1170],{"className":2462},[661],". 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Stimmt ",[568,2705,2706],{},"nicht",[564,2708,2709,2710,602],{},"Also ",[607,2711,2713,2735],{"className":2712},[610],[607,2714,2716],{"className":2715},[614],[616,2717,2718],{"xmlns":618},[620,2719,2720,2732],{},[623,2721,2722,2724,2726,2728,2730],{},[629,2723,1639],{"mathvariant":1638},[633,2725,635],{},[633,2727,1644],{"stretchy":1093},[779,2729,781],{},[633,2731,1649],{"stretchy":1093},[640,2733,2734],{"encoding":642},"\\mathbb{L} = \\{2\\}",[607,2736,2738,2756],{"className":2737,"ariaHidden":648},[647],[607,2739,2741,2744,2747,2750,2753],{"className":2740},[652],[607,2742],{"className":2743,"style":1662},[656],[607,2745,1639],{"className":2746},[661,1666],[607,2748],{"className":2749,"style":737},[736],[607,2751,635],{"className":2752},[741],[607,2754],{"className":2755,"style":737},[736],[607,2757,2759,2762,2765,2768],{"className":2758},[652],[607,2760],{"className":2761,"style":1031},[656],[607,2763,1644],{"className":2764},[1119],[607,2766,781],{"className":2767},[661],[607,2769,1649],{"className":2770},[1126],[564,2772,2773],{},"Erst isolieren:",[607,2775,2777],{"className":2776},[1138],[607,2778,2780,2874],{"className":2779},[610],[607,2781,2783],{"className":2782},[614],[616,2784,2785],{"xmlns":618,"display":1147},[620,2786,2787,2871],{},[623,2788,2789,2793,2795,2797,2799,2801,2803,2805,2807,2811,2813,2815,2817,2819,2821,2823,2825,2827,2829,2835,2837,2839,2841,2843,2845,2847,2849,2851,2857,2859,2861,2863,2865,2867,2869],{},[626,2790,2791],{},[629,2792,1097],{},[633,2794,1717],{},[779,2796,781],{},[633,2798,635],{},[629,2800,1097],{},[1172,2802,1174],{},[633,2804,1177],{},[1172,2806,1174],{},[626,2808,2809],{},[629,2810,1097],{},[633,2812,635],{},[629,2814,1097],{},[633,2816,1162],{},[779,2818,781],{},[1172,2820,1174],{},[633,2822,1177],{},[1172,2824,1174],{},[629,2826,1097],{},[633,2828,635],{},[774,2830,2831,2833],{},[629,2832,1097],{},[779,2834,781],{},[633,2836,1162],{},[779,2838,2537],{},[629,2840,1097],{},[633,2842,1717],{},[779,2844,2537],{},[1172,2846,1174],{},[633,2848,1177],{},[1172,2850,1174],{},[774,2852,2853,2855],{},[629,2854,1097],{},[779,2856,781],{},[633,2858,1162],{},[779,2860,1205],{},[629,2862,1097],{},[633,2864,1717],{},[779,2866,2537],{},[633,2868,635],{},[779,2870,1784],{},[640,2872,2873],{"encoding":642},"\\sqrt{x} + 2 = x \\;\\Rightarrow\\; \\sqrt{x} = x - 2 \\;\\Rightarrow\\; x = x^2 - 4x + 4 \\;\\Rightarrow\\; x^2 - 5x + 4 = 0",[607,2875,2877,2943,2961,2985,3047,3065,3089,3107,3151,3172,3196,3240,3261,3279],{"className":2876,"ariaHidden":648},[647],[607,2878,2880,2884,2934,2937,2940],{"className":2879},[652],[607,2881],{"className":2882,"style":2883},[656],"height:1.04em;vertical-align:-0.1908em;",[607,2885,2887],{"className":2886},[661,662],[607,2888,2890,2925],{"className":2889},[666,667],[607,2891,2893,2922],{"className":2892},[671],[607,2894,2897,2909],{"className":2895,"style":2896},[675],"height:0.8492em;",[607,2898,2900,2903],{"className":2899,"style":681},[680],[607,2901],{"className":2902,"style":686},[685],[607,2904,2906],{"className":2905,"style":690},[661],[607,2907,1097],{"className":2908},[661,694],[607,2910,2912,2915],{"style":2911},"top:-2.8092em;",[607,2913],{"className":2914,"style":686},[685],[607,2916,2918],{"className":2917,"style":706},[705],[708,2919,2920],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,2921],{"d":718},[607,2923,723],{"className":2924},[722],[607,2926,2928],{"className":2927},[671],[607,2929,2932],{"className":2930,"style":2931},[675],"height:0.1908em;",[607,2933],{},[607,2935],{"className":2936,"style":1250},[736],[607,2938,1717],{"className":2939},[1254],[607,2941],{"className":2942,"style":1250},[736],[607,2944,2946,2949,2952,2955,2958],{"className":2945},[652],[607,2947],{"className":2948,"style":1301},[656],[607,2950,781],{"className":2951},[661],[607,2953],{"className":2954,"style":737},[736],[607,2956,635],{"className":2957},[741],[607,2959],{"className":2960,"style":737},[736],[607,2962,2964,2967,2970,2973,2976,2979,2982],{"className":2963},[652],[607,2965],{"className":2966,"style":1390},[656],[607,2968,1097],{"className":2969},[661,694],[607,2971],{"className":2972,"style":737},[736],[607,2974],{"className":2975,"style":737},[736],[607,2977,1177],{"className":2978},[741],[607,2980],{"className":2981,"style":737},[736],[607,2983],{"className":2984,"style":737},[736],[607,2986,2988,2991,3038,3041,3044],{"className":2987},[652],[607,2989],{"className":2990,"style":2883},[656],[607,2992,2994],{"className":2993},[661,662],[607,2995,2997,3030],{"className":2996},[666,667],[607,2998,3000,3027],{"className":2999},[671],[607,3001,3003,3015],{"className":3002,"style":2896},[675],[607,3004,3006,3009],{"className":3005,"style":681},[680],[607,3007],{"className":3008,"style":686},[685],[607,3010,3012],{"className":3011,"style":690},[661],[607,3013,1097],{"className":3014},[661,694],[607,3016,3017,3020],{"style":2911},[607,3018],{"className":3019,"style":686},[685],[607,3021,3023],{"className":3022,"style":706},[705],[708,3024,3025],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,3026],{"d":718},[607,3028,723],{"className":3029},[722],[607,3031,3033],{"className":3032},[671],[607,3034,3036],{"className":3035,"style":2931},[675],[607,3037],{},[607,3039],{"className":3040,"style":737},[736],[607,3042,635],{"className":3043},[741],[607,3045],{"className":3046,"style":737},[736],[607,3048,3050,3053,3056,3059,3062],{"className":3049},[652],[607,3051],{"className":3052,"style":1871},[656],[607,3054,1097],{"className":3055},[661,694],[607,3057],{"className":3058,"style":1250},[736],[607,3060,1162],{"className":3061},[1254],[607,3063],{"className":3064,"style":1250},[736],[607,3066,3068,3071,3074,3077,3080,3083,3086],{"className":3067},[652],[607,3069],{"className":3070,"style":1301},[656],[607,3072,781],{"className":3073},[661],[607,3075],{"className":3076,"style":737},[736],[607,3078],{"className":3079,"style":737},[736],[607,3081,1177],{"className":3082},[741],[607,3084],{"className":3085,"style":737},[736],[607,3087],{"className":3088,"style":737},[736],[607,3090,3092,3095,3098,3101,3104],{"className":3091},[652],[607,3093],{"className":3094,"style":1390},[656],[607,3096,1097],{"className":3097},[661,694],[607,3099],{"className":3100,"style":737},[736],[607,3102,635],{"className":3103},[741],[607,3105],{"className":3106,"style":737},[736],[607,3108,3110,3113,3142,3145,3148],{"className":3109},[652],[607,3111],{"className":3112,"style":1950},[656],[607,3114,3116,3119],{"className":3115},[661],[607,3117,1097],{"className":3118},[661,694],[607,3120,3122],{"className":3121},[822],[607,3123,3125],{"className":3124},[666],[607,3126,3128],{"className":3127},[671],[607,3129,3131],{"className":3130,"style":1969},[675],[607,3132,3133,3136],{"style":1972},[607,3134],{"className":3135,"style":838},[685],[607,3137,3139],{"className":3138},[842,843,844,845],[607,3140,781],{"className":3141},[661,845],[607,3143],{"className":3144,"style":1250},[736],[607,3146,1162],{"className":3147},[1254],[607,3149],{"className":3150,"style":1250},[736],[607,3152,3154,3157,3160,3163,3166,3169],{"className":3153},[652],[607,3155],{"className":3156,"style":1326},[656],[607,3158,2537],{"className":3159},[661],[607,3161,1097],{"className":3162},[661,694],[607,3164],{"className":3165,"style":1250},[736],[607,3167,1717],{"className":3168},[1254],[607,3170],{"className":3171,"style":1250},[736],[607,3173,3175,3178,3181,3184,3187,3190,3193],{"className":3174},[652],[607,3176],{"className":3177,"style":1301},[656],[607,3179,2537],{"className":3180},[661],[607,3182],{"className":3183,"style":737},[736],[607,3185],{"className":3186,"style":737},[736],[607,3188,1177],{"className":3189},[741],[607,3191],{"className":3192,"style":737},[736],[607,3194],{"className":3195,"style":737},[736],[607,3197,3199,3202,3231,3234,3237],{"className":3198},[652],[607,3200],{"className":3201,"style":1950},[656],[607,3203,3205,3208],{"className":3204},[661],[607,3206,1097],{"className":3207},[661,694],[607,3209,3211],{"className":3210},[822],[607,3212,3214],{"className":3213},[666],[607,3215,3217],{"className":3216},[671],[607,3218,3220],{"className":3219,"style":1969},[675],[607,3221,3222,3225],{"style":1972},[607,3223],{"className":3224,"style":838},[685],[607,3226,3228],{"className":3227},[842,843,844,845],[607,3229,781],{"className":3230},[661,845],[607,3232],{"className":3233,"style":1250},[736],[607,3235,1162],{"className":3236},[1254],[607,3238],{"className":3239,"style":1250},[736],[607,3241,3243,3246,3249,3252,3255,3258],{"className":3242},[652],[607,3244],{"className":3245,"style":1326},[656],[607,3247,1205],{"className":3248},[661],[607,3250,1097],{"className":3251},[661,694],[607,3253],{"className":3254,"style":1250},[736],[607,3256,1717],{"className":3257},[1254],[607,3259],{"className":3260,"style":1250},[736],[607,3262,3264,3267,3270,3273,3276],{"className":3263},[652],[607,3265],{"className":3266,"style":1301},[656],[607,3268,2537],{"className":3269},[661],[607,3271],{"className":3272,"style":737},[736],[607,3274,635],{"className":3275},[741],[607,3277],{"className":3278,"style":737},[736],[607,3280,3282,3285],{"className":3281},[652],[607,3283],{"className":3284,"style":1301},[656],[607,3286,1784],{"className":3287},[661],[564,3289,3290,3291,2179,3342,3393,3394,3513,3514,3697,3698,602],{},"Lösungen ",[607,3292,3294,3312],{"className":3293},[610],[607,3295,3297],{"className":3296},[614],[616,3298,3299],{"xmlns":618},[620,3300,3301,3309],{},[623,3302,3303,3305,3307],{},[629,3304,1097],{},[633,3306,635],{},[779,3308,1165],{},[640,3310,3311],{"encoding":642},"x = 1",[607,3313,3315,3333],{"className":3314,"ariaHidden":648},[647],[607,3316,3318,3321,3324,3327,3330],{"className":3317},[652],[607,3319],{"className":3320,"style":1390},[656],[607,3322,1097],{"className":3323},[661,694],[607,3325],{"className":3326,"style":737},[736],[607,3328,635],{"className":3329},[741],[607,3331],{"className":3332,"style":737},[736],[607,3334,3336,3339],{"className":3335},[652],[607,3337],{"className":3338,"style":1301},[656],[607,3340,1165],{"className":3341},[661],[607,3343,3345,3363],{"className":3344},[610],[607,3346,3348],{"className":3347},[614],[616,3349,3350],{"xmlns":618},[620,3351,3352,3360],{},[623,3353,3354,3356,3358],{},[629,3355,1097],{},[633,3357,635],{},[779,3359,2537],{},[640,3361,3362],{"encoding":642},"x = 4",[607,3364,3366,3384],{"className":3365,"ariaHidden":648},[647],[607,3367,3369,3372,3375,3378,3381],{"className":3368},[652],[607,3370],{"className":3371,"style":1390},[656],[607,3373,1097],{"className":3374},[661,694],[607,3376],{"className":3377,"style":737},[736],[607,3379,635],{"className":3380},[741],[607,3382],{"className":3383,"style":737},[736],[607,3385,3387,3390],{"className":3386},[652],[607,3388],{"className":3389,"style":1301},[656],[607,3391,2537],{"className":3392},[661],". Probe: ",[607,3395,3397,3421],{"className":3396},[610],[607,3398,3400],{"className":3399},[614],[616,3401,3402],{"xmlns":618},[620,3403,3404,3418],{},[623,3405,3406,3410,3412,3414,3416],{},[626,3407,3408],{},[779,3409,2537],{},[633,3411,1717],{},[779,3413,781],{},[633,3415,635],{},[779,3417,2537],{},[640,3419,3420],{"encoding":642},"\\sqrt{4} + 2 = 4",[607,3422,3424,3486,3504],{"className":3423,"ariaHidden":648},[647],[607,3425,3427,3430,3477,3480,3483],{"className":3426},[652],[607,3428],{"className":3429,"style":1554},[656],[607,3431,3433],{"className":3432},[661,662],[607,3434,3436,3469],{"className":3435},[666,667],[607,3437,3439,3466],{"className":3438},[671],[607,3440,3442,3454],{"className":3441,"style":1567},[675],[607,3443,3445,3448],{"className":3444,"style":681},[680],[607,3446],{"className":3447,"style":686},[685],[607,3449,3451],{"className":3450,"style":690},[661],[607,3452,2537],{"className":3453},[661],[607,3455,3456,3459],{"style":1582},[607,3457],{"className":3458,"style":686},[685],[607,3460,3462],{"className":3461,"style":706},[705],[708,3463,3464],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,3465],{"d":718},[607,3467,723],{"className":3468},[722],[607,3470,3472],{"className":3471},[671],[607,3473,3475],{"className":3474,"style":1602},[675],[607,3476],{},[607,3478],{"className":3479,"style":1250},[736],[607,3481,1717],{"className":3482},[1254],[607,3484],{"className":3485,"style":1250},[736],[607,3487,3489,3492,3495,3498,3501],{"className":3488},[652],[607,3490],{"className":3491,"style":1301},[656],[607,3493,781],{"className":3494},[661],[607,3496],{"className":3497,"style":737},[736],[607,3499,635],{"className":3500},[741],[607,3502],{"className":3503,"style":737},[736],[607,3505,3507,3510],{"className":3506},[652],[607,3508],{"className":3509,"style":1301},[656],[607,3511,2537],{"className":3512},[661]," stimmt, ",[607,3515,3517,3546],{"className":3516},[610],[607,3518,3520],{"className":3519},[614],[616,3521,3522],{"xmlns":618},[620,3523,3524,3543],{},[623,3525,3526,3530,3532,3534,3536,3538,3541],{},[626,3527,3528],{},[779,3529,1165],{},[633,3531,1717],{},[779,3533,781],{},[633,3535,635],{},[779,3537,1170],{},[633,3539,3540],{"mathvariant":951},"≠",[779,3542,1165],{},[640,3544,3545],{"encoding":642},"\\sqrt{1} + 2 = 3 \\neq 1",[607,3547,3549,3611,3629,3688],{"className":3548,"ariaHidden":648},[647],[607,3550,3552,3555,3602,3605,3608],{"className":3551},[652],[607,3553],{"className":3554,"style":1554},[656],[607,3556,3558],{"className":3557},[661,662],[607,3559,3561,3594],{"className":3560},[666,667],[607,3562,3564,3591],{"className":3563},[671],[607,3565,3567,3579],{"className":3566,"style":1567},[675],[607,3568,3570,3573],{"className":3569,"style":681},[680],[607,3571],{"className":3572,"style":686},[685],[607,3574,3576],{"className":3575,"style":690},[661],[607,3577,1165],{"className":3578},[661],[607,3580,3581,3584],{"style":1582},[607,3582],{"className":3583,"style":686},[685],[607,3585,3587],{"className":3586,"style":706},[705],[708,3588,3589],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,3590],{"d":718},[607,3592,723],{"className":3593},[722],[607,3595,3597],{"className":3596},[671],[607,3598,3600],{"className":3599,"style":1602},[675],[607,3601],{},[607,3603],{"className":3604,"style":1250},[736],[607,3606,1717],{"className":3607},[1254],[607,3609],{"className":3610,"style":1250},[736],[607,3612,3614,3617,3620,3623,3626],{"className":3613},[652],[607,3615],{"className":3616,"style":1301},[656],[607,3618,781],{"className":3619},[661],[607,3621],{"className":3622,"style":737},[736],[607,3624,635],{"className":3625},[741],[607,3627],{"className":3628,"style":737},[736],[607,3630,3632,3636,3639,3642,3685],{"className":3631},[652],[607,3633],{"className":3634,"style":3635},[656],"height:0.8889em;vertical-align:-0.1944em;",[607,3637,1170],{"className":3638},[661],[607,3640],{"className":3641,"style":737},[736],[607,3643,3645,3678,3682],{"className":3644},[741],[607,3646,3648],{"className":3647},[741],[607,3649,3652],{"className":3650},[661,3651],"vbox",[607,3653,3656],{"className":3654},[3655],"thinbox",[607,3657,3660,3663,3674],{"className":3658},[3659],"rlap",[607,3661],{"className":3662,"style":3635},[656],[607,3664,3667],{"className":3665},[3666],"inner",[607,3668,3670],{"className":3669},[661],[607,3671,3673],{"className":3672},[741],"",[607,3675],{"className":3676},[3677],"fix",[607,3679],{"className":3680},[736,3681],"nobreak",[607,3683,635],{"className":3684},[741],[607,3686],{"className":3687,"style":737},[736],[607,3689,3691,3694],{"className":3690},[652],[607,3692],{"className":3693,"style":1301},[656],[607,3695,1165],{"className":3696},[661]," nicht. Also ",[607,3699,3701,3723],{"className":3700},[610],[607,3702,3704],{"className":3703},[614],[616,3705,3706],{"xmlns":618},[620,3707,3708,3720],{},[623,3709,3710,3712,3714,3716,3718],{},[629,3711,1639],{"mathvariant":1638},[633,3713,635],{},[633,3715,1644],{"stretchy":1093},[779,3717,2537],{},[633,3719,1649],{"stretchy":1093},[640,3721,3722],{"encoding":642},"\\mathbb{L} = \\{4\\}",[607,3724,3726,3744],{"className":3725,"ariaHidden":648},[647],[607,3727,3729,3732,3735,3738,3741],{"className":3728},[652],[607,3730],{"className":3731,"style":1662},[656],[607,3733,1639],{"className":3734},[661,1666],[607,3736],{"className":3737,"style":737},[736],[607,3739,635],{"className":3740},[741],[607,3742],{"className":3743,"style":737},[736],[607,3745,3747,3750,3753,3756],{"className":3746},[652],[607,3748],{"className":3749,"style":1031},[656],[607,3751,1644],{"className":3752},[1119],[607,3754,2537],{"className":3755},[661],[607,3757,1649],{"className":3758},[1126],[559,3760,3762],{"id":3761},"typische-fehler","Typische Fehler",[2238,3764,3765,3824,4091],{},[576,3766,3767,3768,3823],{},"Die Probe weglassen und die Scheinlösung ",[607,3769,3771,3790],{"className":3770},[610],[607,3772,3774],{"className":3773},[614],[616,3775,3776],{"xmlns":618},[620,3777,3778,3788],{},[623,3779,3780,3782,3784,3786],{},[629,3781,1097],{},[633,3783,635],{},[633,3785,1162],{},[779,3787,1170],{},[640,3789,2202],{"encoding":642},[607,3791,3793,3811],{"className":3792,"ariaHidden":648},[647],[607,3794,3796,3799,3802,3805,3808],{"className":3795},[652],[607,3797],{"className":3798,"style":1390},[656],[607,3800,1097],{"className":3801},[661,694],[607,3803],{"className":3804,"style":737},[736],[607,3806,635],{"className":3807},[741],[607,3809],{"className":3810,"style":737},[736],[607,3812,3814,3817,3820],{"className":3813},[652],[607,3815],{"className":3816,"style":1326},[656],[607,3818,1162],{"className":3819},[661],[607,3821,1170],{"className":3822},[661]," mit angeben.",[576,3825,3826,3827,4090],{},"Quadrieren, bevor die Wurzel allein steht: ",[607,3828,3830,3876],{"className":3829},[610],[607,3831,3833],{"className":3832},[614],[616,3834,3835],{"xmlns":618},[620,3836,3837,3873],{},[623,3838,3839,3857,3859,3861,3863,3865,3869,3871],{},[774,3840,3841,3855],{},[623,3842,3843,3845,3849,3851,3853],{},[633,3844,1094],{"fence":648},[626,3846,3847],{},[629,3848,1097],{},[633,3850,1717],{},[779,3852,781],{},[633,3854,1100],{"fence":648},[779,3856,781],{},[633,3858,635],{},[629,3860,1097],{},[633,3862,1717],{},[779,3864,2537],{},[626,3866,3867],{},[629,3868,1097],{},[633,3870,1717],{},[779,3872,2537],{},[640,3874,3875],{"encoding":642},"\\left(\\sqrt{x} + 2\\right)^2 = x + 4\\sqrt{x} + 4",[607,3877,3879,3997,4015,4081],{"className":3878,"ariaHidden":648},[647],[607,3880,3882,3886,3988,3991,3994],{"className":3881},[652],[607,3883],{"className":3884,"style":3885},[656],"height:1.2543em;vertical-align:-0.25em;",[607,3887,3890,3963],{"className":3888},[3889],"minner",[607,3891,3893,3898,3948,3951,3954,3957,3960],{"className":3892},[3889],[607,3894,1094],{"className":3895,"style":3897},[1119,3896],"delimcenter","top:0em;",[607,3899,3901],{"className":3900},[661,662],[607,3902,3904,3939],{"className":3903},[666,667],[607,3905,3907,3936],{"className":3906},[671],[607,3908,3911,3923],{"className":3909,"style":3910},[675],"height:0.8003em;",[607,3912,3914,3917],{"className":3913,"style":681},[680],[607,3915],{"className":3916,"style":686},[685],[607,3918,3920],{"className":3919,"style":690},[661],[607,3921,1097],{"className":3922},[661,694],[607,3924,3926,3929],{"style":3925},"top:-2.7603em;",[607,3927],{"className":3928,"style":686},[685],[607,3930,3932],{"className":3931,"style":706},[705],[708,3933,3934],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,3935],{"d":718},[607,3937,723],{"className":3938},[722],[607,3940,3942],{"className":3941},[671],[607,3943,3946],{"className":3944,"style":3945},[675],"height:0.2397em;",[607,3947],{},[607,3949],{"className":3950,"style":1250},[736],[607,3952,1717],{"className":3953},[1254],[607,3955],{"className":3956,"style":1250},[736],[607,3958,781],{"className":3959},[661],[607,3961,1100],{"className":3962,"style":3897},[1126,3896],[607,3964,3966],{"className":3965},[822],[607,3967,3969],{"className":3968},[666],[607,3970,3972],{"className":3971},[671],[607,3973,3976],{"className":3974,"style":3975},[675],"height:1.0043em;",[607,3977,3979,3982],{"style":3978},"top:-3.2532em;margin-right:0.05em;",[607,3980],{"className":3981,"style":838},[685],[607,3983,3985],{"className":3984},[842,843,844,845],[607,3986,781],{"className":3987},[661,845],[607,3989],{"className":3990,"style":737},[736],[607,3992,635],{"className":3993},[741],[607,3995],{"className":3996,"style":737},[736],[607,3998,4000,4003,4006,4009,4012],{"className":3999},[652],[607,4001],{"className":4002,"style":1871},[656],[607,4004,1097],{"className":4005},[661,694],[607,4007],{"className":4008,"style":1250},[736],[607,4010,1717],{"className":4011},[1254],[607,4013],{"className":4014,"style":1250},[736],[607,4016,4018,4022,4025,4072,4075,4078],{"className":4017},[652],[607,4019],{"className":4020,"style":4021},[656],"height:1.04em;vertical-align:-0.2397em;",[607,4023,2537],{"className":4024},[661],[607,4026,4028],{"className":4027},[661,662],[607,4029,4031,4064],{"className":4030},[666,667],[607,4032,4034,4061],{"className":4033},[671],[607,4035,4037,4049],{"className":4036,"style":3910},[675],[607,4038,4040,4043],{"className":4039,"style":681},[680],[607,4041],{"className":4042,"style":686},[685],[607,4044,4046],{"className":4045,"style":690},[661],[607,4047,1097],{"className":4048},[661,694],[607,4050,4051,4054],{"style":3925},[607,4052],{"className":4053,"style":686},[685],[607,4055,4057],{"className":4056,"style":706},[705],[708,4058,4059],{"xmlns":710,"width":711,"height":712,"viewBox":713,"preserveAspectRatio":714},[716,4060],{"d":718},[607,4062,723],{"className":4063},[722],[607,4065,4067],{"className":4066},[671],[607,4068,4070],{"className":4069,"style":3945},[675],[607,4071],{},[607,4073],{"className":4074,"style":1250},[736],[607,4076,1717],{"className":4077},[1254],[607,4079],{"className":4080,"style":1250},[736],[607,4082,4084,4087],{"className":4083},[652],[607,4085],{"className":4086,"style":1301},[656],[607,4088,2537],{"className":4089},[661],", die Wurzel ist dann immer noch da.",[576,4092,4093,4094,4288,4289,602],{},"Summanden einzeln quadrieren: ",[607,4095,4097,4141],{"className":4096},[610],[607,4098,4100],{"className":4099},[614],[616,4101,4102],{"xmlns":618},[620,4103,4104,4138],{},[623,4105,4106,4108,4110,4112,4114,4120,4122,4128,4130,4132,4134,4136],{},[633,4107,1094],{"stretchy":1093},[629,4109,1097],{},[633,4111,1717],{},[779,4113,1165],{},[774,4115,4116,4118],{},[633,4117,1100],{"stretchy":1093},[779,4119,781],{},[633,4121,635],{},[774,4123,4124,4126],{},[629,4125,1097],{},[779,4127,781],{},[633,4129,1717],{},[779,4131,781],{},[629,4133,1097],{},[633,4135,1717],{},[779,4137,1165],{},[640,4139,4140],{"encoding":642},"(x + 1)^2 = x^2 + 2x + 1",[607,4142,4144,4165,4213,4258,4279],{"className":4143,"ariaHidden":648},[647],[607,4145,4147,4150,4153,4156,4159,4162],{"className":4146},[652],[607,4148],{"className":4149,"style":1031},[656],[607,4151,1094],{"className":4152},[1119],[607,4154,1097],{"className":4155},[661,694],[607,4157],{"className":4158,"style":1250},[736],[607,4160,1717],{"className":4161},[1254],[607,4163],{"className":4164,"style":1250},[736],[607,4166,4168,4172,4175,4204,4207,4210],{"className":4167},[652],[607,4169],{"className":4170,"style":4171},[656],"height:1.0641em;vertical-align:-0.25em;",[607,4173,1165],{"className":4174},[661],[607,4176,4178,4181],{"className":4177},[1126],[607,4179,1100],{"className":4180},[1126],[607,4182,4184],{"className":4183},[822],[607,4185,4187],{"className":4186},[666],[607,4188,4190],{"className":4189},[671],[607,4191,4193],{"className":4192,"style":812},[675],[607,4194,4195,4198],{"style":834},[607,4196],{"className":4197,"style":838},[685],[607,4199,4201],{"className":4200},[842,843,844,845],[607,4202,781],{"className":4203},[661,845],[607,4205],{"className":4206,"style":737},[736],[607,4208,635],{"className":4209},[741],[607,4211],{"className":4212,"style":737},[736],[607,4214,4216,4220,4249,4252,4255],{"className":4215},[652],[607,4217],{"className":4218,"style":4219},[656],"height:0.8974em;vertical-align:-0.0833em;",[607,4221,4223,4226],{"className":4222},[661],[607,4224,1097],{"className":4225},[661,694],[607,4227,4229],{"className":4228},[822],[607,4230,4232],{"className":4231},[666],[607,4233,4235],{"className":4234},[671],[607,4236,4238],{"className":4237,"style":812},[675],[607,4239,4240,4243],{"style":834},[607,4241],{"className":4242,"style":838},[685],[607,4244,4246],{"className":4245},[842,843,844,845],[607,4247,781],{"className":4248},[661,845],[607,4250],{"className":4251,"style":1250},[736],[607,4253,1717],{"className":4254},[1254],[607,4256],{"className":4257,"style":1250},[736],[607,4259,4261,4264,4267,4270,4273,4276],{"className":4260},[652],[607,4262],{"className":4263,"style":1326},[656],[607,4265,781],{"className":4266},[661],[607,4268,1097],{"className":4269},[661,694],[607,4271],{"className":4272,"style":1250},[736],[607,4274,1717],{"className":4275},[1254],[607,4277],{"className":4278,"style":1250},[736],[607,4280,4282,4285],{"className":4281},[652],[607,4283],{"className":4284,"style":1301},[656],[607,4286,1165],{"className":4287},[661],", nicht ",[607,4290,4292,4314],{"className":4291},[610],[607,4293,4295],{"className":4294},[614],[616,4296,4297],{"xmlns":618},[620,4298,4299,4311],{},[623,4300,4301,4307,4309],{},[774,4302,4303,4305],{},[629,4304,1097],{},[779,4306,781],{},[633,4308,1717],{},[779,4310,1165],{},[640,4312,4313],{"encoding":642},"x^2 + 1",[607,4315,4317,4361],{"className":4316,"ariaHidden":648},[647],[607,4318,4320,4323,4352,4355,4358],{"className":4319},[652],[607,4321],{"className":4322,"style":4219},[656],[607,4324,4326,4329],{"className":4325},[661],[607,4327,1097],{"className":4328},[661,694],[607,4330,4332],{"className":4331},[822],[607,4333,4335],{"className":4334},[666],[607,4336,4338],{"className":4337},[671],[607,4339,4341],{"className":4340,"style":812},[675],[607,4342,4343,4346],{"style":834},[607,4344],{"className":4345,"style":838},[685],[607,4347,4349],{"className":4348},[842,843,844,845],[607,4350,781],{"className":4351},[661,845],[607,4353],{"className":4354,"style":1250},[736],[607,4356,1717],{"className":4357},[1254],[607,4359],{"className":4360,"style":1250},[736],[607,4362,4364,4367],{"className":4363},[652],[607,4365],{"className":4366,"style":1301},[656],[607,4368,1165],{"className":4369},[661],{"title":4371,"searchDepth":4372,"depth":4372,"links":4373},"",2,[4374,4375,4376],{"id":561,"depth":4372,"text":562},{"id":1130,"depth":4372,"text":1131},{"id":3761,"depth":4372,"text":3762},[4378,4381,4383,4385,4388,4390,4393,4395,4398,4401,4403,4405,4407,4410],{"lhs":4379,"rhs":4380},"sqrt(t)^2","t",{"lhs":4382,"rhs":1205},"(9 + 1)\u002F2",{"lhs":4384,"rhs":1170},"sqrt(2*5 - 1)",{"lhs":4386,"rhs":4387},"(x + 1)^2 - (x + 7)","x^2 + x - 6",{"lhs":4387,"rhs":4389},"(x - 2)*(x + 3)",{"lhs":4391,"rhs":4392},"sqrt(2 + 7)","2 + 1",{"lhs":4394,"rhs":781},"sqrt(-3 + 7)",{"lhs":4396,"rhs":4397},"-3 + 1","-2",{"lhs":4399,"rhs":4400},"(x - 2)^2 - x","x^2 - 5*x + 4",{"lhs":4400,"rhs":4402},"(x - 1)*(x - 4)",{"lhs":4404,"rhs":2537},"sqrt(4) + 2",{"lhs":4406,"rhs":1170},"sqrt(1) + 2",{"lhs":4408,"rhs":4409},"(sqrt(x) + 2)^2","x + 4*sqrt(x) + 4",{"lhs":4411,"rhs":4412},"(x + 1)^2","x^2 + 2*x + 1","T(x) \\geq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>T\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">T(x) \\geq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","root-equation","\\sqrt{T(x)} = S(x) \\;\\Rightarrow\\; T(x) = S(x)^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsqrt>\u003Cmrow>\u003Cmi>T\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>S\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>T\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>S\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sqrt{T(x)} = S(x) \\;\\Rightarrow\\; T(x) = S(x)^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.24em;vertical-align:-0.2561em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9839em;\">\u003Cspan class=\"svg-align\" style=\"top:-3.2em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:1em;\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9439em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2561em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan 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