x^3= 64/729

解

x^{3} = \frac{64}{729}

x = \frac{4}{9}, x = - \frac{2}{9} + \frac{2}{3 3} i, x = - \frac{2}{9} - \frac{2}{3 3} i

解答ステップ

x^{3} = \frac{64}{729}

x^{3} = f (a)

では, 解は

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{64}{729}, x = 3 \frac{64}{729} \frac{- 1 + 3 i}{2}, x = 3 \frac{64}{729} \frac{- 1 - 3 i}{2}

3 \frac{64}{729} = \frac{4}{9}

簡素化

3 \frac{64}{729} \frac{- 1 + 3 i}{2} : - \frac{2}{9} + \frac{2}{3 3} i

簡素化

3 \frac{64}{729} \frac{- 1 - 3 i}{2} : - \frac{2}{9} - \frac{2}{3 3} i

x = \frac{4}{9}, x = - \frac{2}{9} + \frac{2}{3 3} i, x = - \frac{2}{9} - \frac{2}{3 3} i