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受欢迎的代数 >

x^6+8=26

解答

x^{6} + 8 = 26

解答

x = 318, x = - 318, x = 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i

求解步骤

x^{6} + 8 = 26

将

8

到右边

x^{6} = 18

用

u = x^{2}

和

u^{3} = x^{6}

改写方程式

u^{3} = 18

解

u^{3} = 18 : u = 318, u = 318 \frac{- 1 + 3 i}{2}, u = 318 \frac{- 1 - 3 i}{2}

u = 318, u = 318 \frac{- 1 + 3 i}{2}, u = 318 \frac{- 1 - 3 i}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 318 : x = 318, x = - 318

解

x^{2} = 318 \frac{- 1 + 3 i}{2} : x = 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i

解

x^{2} = 318 \frac{- 1 - 3 i}{2} : x = 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i

解为

x = 318, x = - 318, x = 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = 0.80943 \dots - \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i, x = - 0.80943 \dots + \frac{3 3 9}{2 ^{\frac{2}{3}} \cdot 1.61887 \dots} i

作图

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