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受欢迎的代数 >

b^6+7b^3-8=0

解答

b^{6} + 7 b^{3} - 8 = 0

解答

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

求解步骤

b^{6} + 7 b^{3} - 8 = 0

用

u = b^{3}

和

u^{2} = b^{6}

改写方程式

u^{2} + 7 u - 8 = 0

解

u^{2} + 7 u - 8 = 0 : u = 1, u = - 8

u = 1, u = - 8

代回

u = b^{3}

，求解

b

解

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

解

b^{3} = - 8 : b = - 2, b = 1 - 3 i, b = 1 + 3 i

解为

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

作图

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