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受欢迎的代数 >

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

解答

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

解答

x = \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i, x = \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i

求解步骤

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

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

6 u^{2} - 4 u + 2 = 0

解

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

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

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{1}{3} + i \frac{2}{3} : x = \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i

解

x^{2} = \frac{1}{3} - i \frac{2}{3} : x = \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i

解为

x = \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i, x = \frac{1 + 3}{6} - \frac{1}{3 1 + 3} i, x = - \frac{1 + 3}{6} + \frac{1}{3 1 + 3} i

作图

流行的例子

1024 = r^{5}

x^3-2x^2-15x+36=0

x^{3} - 2 x^{2} - 15 x + 36 = 0

r^{5} = 32

8x^3+14x^2-5x-2=0

8 x^{3} + 14 x^{2} - 5 x - 2 = 0

0 = 9 y - y^{3}