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受欢迎的代数 >

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

解答

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

解答

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

求解步骤

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

用

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

和

u^{3} = x^{6}

改写方程式

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

解

3 u^{3} - u^{2} - 12 u + 4 = 0 : u = \frac{1}{3}, u = - 2, u = 2

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

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{1}{3} : x = \frac{1}{3}, x = - \frac{1}{3}

解

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

解

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

解为

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

作图

流行的例子

m^3+3m^2-4m-12=0

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

16x^3-48x^2-25x+75=0

16 x^{3} - 48 x^{2} - 25 x + 75 = 0

42 x^{5} - 210 x^{4} = 0

x^{2} (1 - x) = 0

0 = x^{3} + 2 x - 1