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受欢迎的代数 >

256/625 =100r^6

解答

\frac{256}{625} = 100 r^{6}

解答

r = \frac{2}{5}, r = - \frac{2}{5}, r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i, r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

求解步骤

\frac{256}{625} = 100 r^{6}

交换两边

100 r^{6} = \frac{256}{625}

两边除以

100

r^{6} = \frac{64}{15625}

用

u = r^{2}

和

u^{3} = r^{6}

改写方程式

u^{3} = \frac{64}{15625}

解

u^{3} = \frac{64}{15625} : u = 3 \frac{64}{15625}, u = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2}, u = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2}

u = 3 \frac{64}{15625}, u = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2}, u = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2}

代回

u = r^{2}

，求解

r

解

r^{2} = 3 \frac{64}{15625} : r = \frac{2}{5}, r = - \frac{2}{5}

解

r^{2} = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2} : r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i

解

r^{2} = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2} : r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

解为

r = \frac{2}{5}, r = - \frac{2}{5}, r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i, r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

作图

流行的例子

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