x^3=-512

解

x^{3} = - 512

x = - 8, x = 4 - 43 i, x = 4 + 43 i

解答ステップ

x^{3} = - 512

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 - 512, x = 3 - 512 \frac{- 1 + 3 i}{2}, x = 3 - 512 \frac{- 1 - 3 i}{2}

3 - 512 = - 8

簡素化

3 - 512 \frac{- 1 + 3 i}{2} : 4 - 43 i

簡素化

3 - 512 \frac{- 1 - 3 i}{2} : 4 + 43 i

x = - 8, x = 4 - 43 i, x = 4 + 43 i