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受欢迎的代数 >

a^{20}=asqrt(2)

解答

a^{20} = a 2

解答

a = 0, a = 382

+1

十进制

a = 0, a = 1.01840 \dots

求解步骤

a^{20} = a 2

将

a 2

para o lado esquerdo

a^{20} - a 2 = 0

因式分解

a^{20} - a 2 : a (a - 382) (a^{18} + 382 a^{17} + 192 a^{16} + 2^{\frac{3}{38}} a^{15} + 2^{\frac{2}{19}} a^{14} + 2^{\frac{5}{38}} a^{13} + 2^{\frac{3}{19}} a^{12} + 2^{\frac{7}{38}} a^{11} + 2^{\frac{4}{19}} a^{10} + 2^{\frac{9}{38}} a^{9} + 2^{\frac{5}{19}} a^{8} + 2^{\frac{11}{38}} a^{7} + 2^{\frac{6}{19}} a^{6} + 2^{\frac{13}{38}} a^{5} + 2^{\frac{7}{19}} a^{4} + 2^{\frac{15}{38}} a^{3} + 2^{\frac{8}{19}} a^{2} + 2^{\frac{17}{38}} a + 2^{\frac{9}{19}})

a (a - 382) (a^{18} + 382 a^{17} + 192 a^{16} + 2^{\frac{3}{38}} a^{15} + 2^{\frac{2}{19}} a^{14} + 2^{\frac{5}{38}} a^{13} + 2^{\frac{3}{19}} a^{12} + 2^{\frac{7}{38}} a^{11} + 2^{\frac{4}{19}} a^{10} + 2^{\frac{9}{38}} a^{9} + 2^{\frac{5}{19}} a^{8} + 2^{\frac{11}{38}} a^{7} + 2^{\frac{6}{19}} a^{6} + 2^{\frac{13}{38}} a^{5} + 2^{\frac{7}{19}} a^{4} + 2^{\frac{15}{38}} a^{3} + 2^{\frac{8}{19}} a^{2} + 2^{\frac{17}{38}} a + 2^{\frac{9}{19}}) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

a = 0 or a - 382 = 0 or a^{18} + 382 a^{17} + 192 a^{16} + 2^{\frac{3}{38}} a^{15} + 2^{\frac{2}{19}} a^{14} + 2^{\frac{5}{38}} a^{13} + 2^{\frac{3}{19}} a^{12} + 2^{\frac{7}{38}} a^{11} + 2^{\frac{4}{19}} a^{10} + 2^{\frac{9}{38}} a^{9} + 2^{\frac{5}{19}} a^{8} + 2^{\frac{11}{38}} a^{7} + 2^{\frac{6}{19}} a^{6} + 2^{\frac{13}{38}} a^{5} + 2^{\frac{7}{19}} a^{4} + 2^{\frac{15}{38}} a^{3} + 2^{\frac{8}{19}} a^{2} + 2^{\frac{17}{38}} a + 2^{\frac{9}{19}} = 0

解

a - 382 = 0 : a = 382

解

a^{18} + 382 a^{17} + 192 a^{16} + 2^{\frac{3}{38}} a^{15} + 2^{\frac{2}{19}} a^{14} + 2^{\frac{5}{38}} a^{13} + 2^{\frac{3}{19}} a^{12} + 2^{\frac{7}{38}} a^{11} + 2^{\frac{4}{19}} a^{10} + 2^{\frac{9}{38}} a^{9} + 2^{\frac{5}{19}} a^{8} + 2^{\frac{11}{38}} a^{7} + 2^{\frac{6}{19}} a^{6} + 2^{\frac{13}{38}} a^{5} + 2^{\frac{7}{19}} a^{4} + 2^{\frac{15}{38}} a^{3} + 2^{\frac{8}{19}} a^{2} + 2^{\frac{17}{38}} a + 2^{\frac{9}{19}} = 0 : a \in R

无解

解为

a = 0, a = 382

作图

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