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受欢迎的代数 >

x^4-8x^2-9=0

解答

x^{4} - 8 x^{2} - 9 = 0

解答

x = 3, x = - 3, x = i, x = - i

求解步骤

x^{4} - 8 x^{2} - 9 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - 8 u - 9 = 0

解

u^{2} - 8 u - 9 = 0 : u = 9, u = - 1

u = 9, u = - 1

代回

u = x^{2}

，求解

x

解

x^{2} = 9 : x = 3, x = - 3

解

x^{2} = - 1 : x = i, x = - i

解为

x = 3, x = - 3, x = i, x = - i

作图

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