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受欢迎的代数 >

x^6-3x^4+4x^2-12=0

解答

x^{6} - 3 x^{4} + 4 x^{2} - 12 = 0

解答

x = 3, x = - 3, x = 1 + i, x = - 1 - i, x = 1 - i, x = - 1 + i

求解步骤

x^{6} - 3 x^{4} + 4 x^{2} - 12 = 0

用

u = x^{2}, u^{2} = x^{4}

和

u^{3} = x^{6}

改写方程式

u^{3} - 3 u^{2} + 4 u - 12 = 0

解

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

u = 3, u = 2 i, u = - 2 i

代回

u = x^{2}

，求解

x

解

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

解

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

解

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

解为

x = 3, x = - 3, x = 1 + i, x = - 1 - i, x = 1 - i, x = - 1 + i

作图

流行的例子

4x^3+6x^2-6x-4=0

4 x^{3} + 6 x^{2} - 6 x - 4 = 0

x^{4} + 2 x^{2} - 15 = 0

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- x^{3} + 3 x^{2} + 9 x + 5 = 0

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

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