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受欢迎的代数 >

x^6=4096

解答

x^{6} = 4096

解答

x = 4, x = - 4, x = 2 + 23 i, x = - 2 - 23 i, x = 2 - 23 i, x = - 2 + 23 i

求解步骤

x^{6} = 4096

用

u = x^{2}

和

u^{3} = x^{6}

改写方程式

u^{3} = 4096

解

u^{3} = 4096 : u = 34096, u = 34096 \frac{- 1 + 3 i}{2}, u = 34096 \frac{- 1 - 3 i}{2}

u = 34096, u = 34096 \frac{- 1 + 3 i}{2}, u = 34096 \frac{- 1 - 3 i}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 34096 : x = 4, x = - 4

解

x^{2} = 34096 \frac{- 1 + 3 i}{2} : x = 2 + 23 i, x = - 2 - 23 i

解

x^{2} = 34096 \frac{- 1 - 3 i}{2} : x = 2 - 23 i, x = - 2 + 23 i

解为

x = 4, x = - 4, x = 2 + 23 i, x = - 2 - 23 i, x = 2 - 23 i, x = - 2 + 23 i

作图

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