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受欢迎的代数 >

125000(x)^6=165000

解答

125000 (x)^{6} = 165000

解答

x = 3 \frac{33}{25}, x = - 3 \frac{33}{25}, x = 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i

求解步骤

125000 x^{6} = 165000

两边除以

125000

x^{6} = \frac{33}{25}

用

u = x^{2}

和

u^{3} = x^{6}

改写方程式

u^{3} = \frac{33}{25}

解

u^{3} = \frac{33}{25} : u = 3 \frac{33}{25}, u = 3 \frac{33}{25} \frac{- 1 + 3 i}{2}, u = 3 \frac{33}{25} \frac{- 1 - 3 i}{2}

u = 3 \frac{33}{25}, u = 3 \frac{33}{25} \frac{- 1 + 3 i}{2}, u = 3 \frac{33}{25} \frac{- 1 - 3 i}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = 3 \frac{33}{25} : x = 3 \frac{33}{25}, x = - 3 \frac{33}{25}

解

x^{2} = 3 \frac{33}{25} \frac{- 1 + 3 i}{2} : x = 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i

解

x^{2} = 3 \frac{33}{25} \frac{- 1 - 3 i}{2} : x = 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i

解为

x = 3 \frac{33}{25}, x = - 3 \frac{33}{25}, x = 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = 0.52367 \dots - \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i, x = - 0.52367 \dots + \frac{3 ^{\frac{5}{6}} 3 11}{2 5 ^{\frac{1}{3}} \cdot 2.09471 \dots} i

作图

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