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受欢迎的代数 >

z^6-2sqrt(3)z^4+4z^2=0

解答

z^{6} - 23 z^{4} + 4 z^{2} = 0

解答

z = 0, z = \frac{3 + 2}{2} + \frac{1}{2 2 + 3} i, z = - \frac{3 + 2}{2} - \frac{1}{2 2 + 3} i, z = \frac{3 + 2}{2} - \frac{1}{2 2 + 3} i, z = - \frac{3 + 2}{2} + \frac{1}{2 2 + 3} i

求解步骤

z^{6} - 23 z^{4} + 4 z^{2} = 0

用

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

和

u^{3} = z^{6}

改写方程式

u^{3} - 23 u^{2} + 4 u = 0

解

u^{3} - 23 u^{2} + 4 u = 0 : u = 0, u = 3 + i, u = 3 - i

u = 0, u = 3 + i, u = 3 - i

代回

u = z^{2}

，求解

z

解

z^{2} = 0 : z = 0

解

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

解

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

解为

z = 0, z = \frac{3 + 2}{2} + \frac{1}{2 2 + 3} i, z = - \frac{3 + 2}{2} - \frac{1}{2 2 + 3} i, z = \frac{3 + 2}{2} - \frac{1}{2 2 + 3} i, z = - \frac{3 + 2}{2} + \frac{1}{2 2 + 3} i

作图

流行的例子

x^3+2x^2+9x+18=0

x^{3} + 2 x^{2} + 9 x + 18 = 0

z^{3} - 8 = 0

2x^4-47x^2-75=0

2 x^{4} - 47 x^{2} - 75 = 0

solvefor y,x=y^5

so l v e f or y, x = y^{5}

x^{6} = 2