(x^8-x^2)/(x^4-x^2)=9

解

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} = 9

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

解答ステップ

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} = 9

簡素化

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} : x^{4} + x^{2} + 1

x^{4} + x^{2} + 1 = 9

解く

x^{4} + x^{2} + 1 = 9 : x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}

解を検算する

未定義の (特異) 点を求める:

x = 1, x = - 1, x = 0

未定義のポイントを解に組み合わせる:

x = \frac{- 1 + 33}{2}, x = - \frac{- 1 + 33}{2}, x = \frac{- 1 - 33}{2}, x = - \frac{- 1 - 33}{2}