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受欢迎的代数 >

x^6-2=0

解答

x^{6} - 2 = 0

解答

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

求解步骤

x^{6} - 2 = 0

将

2

到右边

x^{6} = 2

用

u = x^{2}

和

u^{3} = x^{6}

改写方程式

u^{3} = 2

解

u^{3} = 2 : u = 32, u = 32 \frac{- 1 + 3 i}{2}, u = 32 \frac{- 1 - 3 i}{2}

u = 32, u = 32 \frac{- 1 + 3 i}{2}, u = 32 \frac{- 1 - 3 i}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 32 : x = 32, x = - 32

解

x^{2} = 32 \frac{- 1 + 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i

解

x^{2} = 32 \frac{- 1 - 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

解为

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

作图

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