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受欢迎的代数 >

x^8-2x^6+2x^4-2x^2+1=0

解答

x^{8} - 2 x^{6} + 2 x^{4} - 2 x^{2} + 1 = 0

解答

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

求解步骤

x^{8} - 2 x^{6} + 2 x^{4} - 2 x^{2} + 1 = 0

用

u = x^{2}, u^{2} = x^{4}, u^{3} = x^{6}

和

u^{4} = x^{8}

改写方程式

u^{4} - 2 u^{3} + 2 u^{2} - 2 u + 1 = 0

解

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

u = 1, u = i, u = - i

代回

u = x^{2}

，求解

x

解

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

解

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

解

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

解为

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

作图

流行的例子

z^{4} + 4 \cdot z^{2} - 45 = 0

x^3-9x^2+24x-19=0

x^{3} - 9 x^{2} + 24 x - 19 = 0

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

x^3-21x^2+111x-11=0

x^{3} - 21 x^{2} + 111 x - 11 = 0

x^4-18x^2=18x^2

x^{4} - 18 x^{2} = 18 x^{2}