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受欢迎的代数 >

(x^4-1)=0

解答

(x^{4} - 1) = 0

解答

x = 1, x = - 1, x = i, x = - i

求解步骤

(x^{4} - 1) = 0

x^{4} - 1 = 0

将

1

到右边

x^{4} = 1

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = 1

解

u^{2} = 1 : u = 1, u = - 1

u = 1, u = - 1

代回

u = x^{2}

，求解

x

解

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

解

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

解为

x = 1, x = - 1, x = i, x = - i

作图

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