x^3+x^{-3}=18,x+1/x

解

x^{3} + x^{- 3} = 18, x + \frac{1}{x}

x = 3 9 + 45, x = - 3 9 + 45 \frac{1}{2} + 3 9 + 45 \frac{3}{2} i, x = - 3 9 + 45 \frac{1}{2} - 3 9 + 45 \frac{3}{2} i, x = 3 9 - 45, x = - 3 9 - 45 \frac{1}{2} + 3 9 - 45 \frac{3}{2} i, x = - 3 9 - 45 \frac{1}{2} - 3 9 - 45 \frac{3}{2} i

解答ステップ

x^{3} + x^{- 3} = 18

改良

x^{3} + \frac{1}{x ^{3}} = 18

以下で両辺を乗じる:

x^{3}

x^{6} + 1 = 18 x^{3}

解く

x^{6} + 1 = 18 x^{3} : x = 3 9 + 45, x = - 3 9 + 45 \frac{1}{2} + 3 9 + 45 \frac{3}{2} i, x = - 3 9 + 45 \frac{1}{2} - 3 9 + 45 \frac{3}{2} i, x = 3 9 - 45, x = - 3 9 - 45 \frac{1}{2} + 3 9 - 45 \frac{3}{2} i, x = - 3 9 - 45 \frac{1}{2} - 3 9 - 45 \frac{3}{2} i

x = 3 9 + 45, x = - 3 9 + 45 \frac{1}{2} + 3 9 + 45 \frac{3}{2} i, x = - 3 9 + 45 \frac{1}{2} - 3 9 + 45 \frac{3}{2} i, x = 3 9 - 45, x = - 3 9 - 45 \frac{1}{2} + 3 9 - 45 \frac{3}{2} i, x = - 3 9 - 45 \frac{1}{2} - 3 9 - 45 \frac{3}{2} i

解を検算する

未定義の (特異) 点を求める:

x = 0

未定義のポイントを解に組み合わせる:

x = 3 9 + 45, x = - 3 9 + 45 \frac{1}{2} + 3 9 + 45 \frac{3}{2} i, x = - 3 9 + 45 \frac{1}{2} - 3 9 + 45 \frac{3}{2} i, x = 3 9 - 45, x = - 3 9 - 45 \frac{1}{2} + 3 9 - 45 \frac{3}{2} i, x = - 3 9 - 45 \frac{1}{2} - 3 9 - 45 \frac{3}{2} i