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受欢迎的代数 >

(x^2-1)^2+(x^2-1)-12=0

解答

(x^{2} - 1)^{2} + (x^{2} - 1) - 12 = 0

解答

x = 2, x = - 2, x = 3 i, x = - 3 i

求解步骤

(x^{2} - 1)^{2} + (x^{2} - 1) - 12 = 0

展开

(x^{2} - 1)^{2} + (x^{2} - 1) - 12 : x^{4} - x^{2} - 12

x^{4} - x^{2} - 12 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} - u - 12 = 0

解

u^{2} - u - 12 = 0 : u = 4, u = - 3

u = 4, u = - 3

代回

u = x^{2}

，求解

x

解

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

解

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

解为

x = 2, x = - 2, x = 3 i, x = - 3 i

作图

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