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受欢迎的代数 >

2x^4+5x^2-3=0

解答

2 x^{4} + 5 x^{2} - 3 = 0

解答

x = \frac{1}{2}, x = - \frac{1}{2}, x = 3 i, x = - 3 i

求解步骤

2 x^{4} + 5 x^{2} - 3 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

2 u^{2} + 5 u - 3 = 0

解

2 u^{2} + 5 u - 3 = 0 : u = \frac{1}{2}, u = - 3

u = \frac{1}{2}, u = - 3

代回

u = x^{2}

，求解

x

解

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

解

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

解为

x = \frac{1}{2}, x = - \frac{1}{2}, x = 3 i, x = - 3 i

作图

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