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受欢迎的代数 >

3x^6-39x^4+108x^2=0

解答

3 x^{6} - 39 x^{4} + 108 x^{2} = 0

解答

x = 0, x = 2, x = - 2, x = 3, x = - 3

求解步骤

3 x^{6} - 39 x^{4} + 108 x^{2} = 0

用

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

和

u^{3} = x^{6}

改写方程式

3 u^{3} - 39 u^{2} + 108 u = 0

解

3 u^{3} - 39 u^{2} + 108 u = 0 : u = 0, u = 4, u = 9

u = 0, u = 4, u = 9

代回

u = x^{2}

，求解

x

解

x^{2} = 0 : x = 0

解

x^{2} = 4 : x = 2, x = - 2

解

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

解为

x = 0, x = 2, x = - 2, x = 3, x = - 3

作图

流行的例子

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r^3-7r^2+16r-12=0

r^{3} - 7 r^{2} + 16 r - 12 = 0

x^{3} + 3 x^{2} - 112 = 0

x^4-6/7 x^2+3/35 =0

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0