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受欢迎的代数 >

x^6-5*3+6=0

解答

x^{6} - 5 \cdot 3 + 6 = 0

解答

x = 39, x = - 39, x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i

求解步骤

x^{6} - 5 \cdot 3 + 6 = 0

将

5 \cdot 3

到右边

x^{6} + 6 = 15

将

6

到右边

x^{6} = 9

用

u = x^{2}

和

u^{3} = x^{6}

改写方程式

u^{3} = 9

解

u^{3} = 9 : u = 39, u = 39 \frac{- 1 + 3 i}{2}, u = 39 \frac{- 1 - 3 i}{2}

u = 39, u = 39 \frac{- 1 + 3 i}{2}, u = 39 \frac{- 1 - 3 i}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 39 : x = 39, x = - 39

解

x^{2} = 39 \frac{- 1 + 3 i}{2} : x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i

解

x^{2} = 39 \frac{- 1 - 3 i}{2} : x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i

解为

x = 39, x = - 39, x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} - \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i, x = - \frac{- 3 9 + 2 9 ^{\frac{2}{3}}}{2} + \frac{3 9 3}{2 - 3 9 + 2 9 ^{\frac{2}{3}}} i

作图

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