-x^3+(x-5)^3+1115=0

解

- x^{3} + (x - 5)^{3} + 1115 = 0

x = - 6, x = 11

解答ステップ

- x^{3} + (x - 5)^{3} + 1115 = 0

拡張

- x^{3} + (x - 5)^{3} + 1115 : - 15 x^{2} + 75 x + 990

- 15 x^{2} + 75 x + 990 = 0

解くとthe二次式

x_{1, 2} = \frac{- 75 \pm 7 5 ^{2} - 4 ( - 15 ) \cdot 990}{2 ( - 15 )}

7 5^{2} - 4 (- 15) \cdot 990 = 255

x_{1, 2} = \frac{- 75 \pm 255}{2 ( - 15 )}

解を分離する

x_{1} = \frac{- 75 + 255}{2 ( - 15 )}, x_{2} = \frac{- 75 - 255}{2 ( - 15 )}

x = \frac{- 75 + 255}{2 ( - 15 )} : - 6

x = \frac{- 75 - 255}{2 ( - 15 )} : 11

二次equationの解:

x = - 6, x = 11