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受欢迎的代数 >

b^6=7

解答

b^{6} = 7

解答

b = 37, b = - 37, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

求解步骤

b^{6} = 7

用

u = b^{2}

和

u^{3} = b^{6}

改写方程式

u^{3} = 7

解

u^{3} = 7 : u = 37, u = 37 \frac{- 1 + 3 i}{2}, u = 37 \frac{- 1 - 3 i}{2}

u = 37, u = 37 \frac{- 1 + 3 i}{2}, u = 37 \frac{- 1 - 3 i}{2}

代回

u = b^{2}

，求解

b

解

b^{2} = 37 : b = 37, b = - 37

解

b^{2} = 37 \frac{- 1 + 3 i}{2} : b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

解

b^{2} = 37 \frac{- 1 - 3 i}{2} : b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

解为

b = 37, b = - 37, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} - \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i, b = - \frac{- 3 7 + 2 7 ^{\frac{2}{3}}}{2} + \frac{3 7 3}{2 - 3 7 + 2 7 ^{\frac{2}{3}}} i

作图

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