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受欢迎的代数 >

4x^4=24x^2+108

解答

4 x^{4} = 24 x^{2} + 108

解答

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

求解步骤

4 x^{4} = 24 x^{2} + 108

将

108

para o lado esquerdo

4 x^{4} - 108 = 24 x^{2}

将

24 x^{2}

para o lado esquerdo

4 x^{4} - 108 - 24 x^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{4} - 24 x^{2} - 108 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

4 u^{2} - 24 u - 108 = 0

解

4 u^{2} - 24 u - 108 = 0 : u = 9, u = - 3

u = 9, u = - 3

代回

u = x^{2}

，求解

x

解

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

解

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

解为

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

作图

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