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受欢迎的代数 >

x^4+3=0

解答

x^{4} + 3 = 0

解答

x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

求解步骤

x^{4} + 3 = 0

将

3

到右边

x^{4} = - 3

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = - 3

解

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

u = 3 i, u = - 3 i

代回

u = x^{2}

，求解

x

解

x^{2} = 3 i : x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i

解

x^{2} = - 3 i : x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

解为

x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

作图

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