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受欢迎的代数 >

8x^6+9x^3+1=0

解答

8 x^{6} + 9 x^{3} + 1 = 0

解答

x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

求解步骤

8 x^{6} + 9 x^{3} + 1 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

8 u^{2} + 9 u + 1 = 0

解

8 u^{2} + 9 u + 1 = 0 : u = - \frac{1}{8}, u = - 1

u = - \frac{1}{8}, u = - 1

代回

u = x^{3}

，求解

x

解

x^{3} = - \frac{1}{8} : x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i

解

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

解为

x = - \frac{1}{2}, x = \frac{1}{4} - \frac{3}{4} i, x = \frac{1}{4} + \frac{3}{4} i, x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i

作图

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