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受欢迎的代数 >

x^6+56x^3-512=0

解答

x^{6} + 56 x^{3} - 512 = 0

解答

x = 2, x = - 1 + 3 i, x = - 1 - 3 i, x = - 4, x = 2 - 23 i, x = 2 + 23 i

求解步骤

x^{6} + 56 x^{3} - 512 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

u^{2} + 56 u - 512 = 0

解

u^{2} + 56 u - 512 = 0 : u = 8, u = - 64

u = 8, u = - 64

代回

u = x^{3}

，求解

x

解

x^{3} = 8 : x = 2, x = - 1 + 3 i, x = - 1 - 3 i

解

x^{3} = - 64 : x = - 4, x = 2 - 23 i, x = 2 + 23 i

解为

x = 2, x = - 1 + 3 i, x = - 1 - 3 i, x = - 4, x = 2 - 23 i, x = 2 + 23 i

作图

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