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人気のある代数 >

solvefor y,y^2=(x-y)(x^2+y)

解

解く

y, y^{2} = (x - y) (x^{2} + y)

解

y = - \frac{- x + x ^{2} + x x ^{2} + 6 x + 1}{4}, y = - \frac{- x + x ^{2} - x x ^{2} + 6 x + 1}{4}

解答ステップ

y^{2} = (x - y) (x^{2} + y)

拡張

(x - y) (x^{2} + y) : x^{3} + y x - y x^{2} - y^{2}

y^{2} = x^{3} + y x - y x^{2} - y^{2}

辺を交換する

x^{3} + y x - y x^{2} - y^{2} = y^{2}

y^{2}

を左側に移動します

x^{3} + y x - y x^{2} - 2 y^{2} = 0

標準的な形式で書く

a x^{2} + b x + c = 0

- 2 y^{2} + (x - x^{2}) y + x^{3} = 0

解くとthe二次式

y_{1, 2} = \frac{- ( x - x ^{2} ) \pm ( x - x ^{2} ) ^{2} - 4 ( - 2 ) x ^{3}}{2 ( - 2 )}

簡素化

(x - x^{2})^{2} - 4 (- 2) x^{3} : x x^{2} + 6 x + 1

y_{1, 2} = \frac{- ( x - x ^{2} ) \pm x x ^{2} + 6 x + 1}{2 ( - 2 )}

解を分離する

y_{1} = \frac{- ( x - x ^{2} ) + x x ^{2} + 6 x + 1}{2 ( - 2 )}, y_{2} = \frac{- ( x - x ^{2} ) - x x ^{2} + 6 x + 1}{2 ( - 2 )}

y = \frac{- ( x - x ^{2} ) + x x ^{2} + 6 x + 1}{2 ( - 2 )} : - \frac{- x + x ^{2} + x x ^{2} + 6 x + 1}{4}

y = \frac{- ( x - x ^{2} ) - x x ^{2} + 6 x + 1}{2 ( - 2 )} : - \frac{- x + x ^{2} - x x ^{2} + 6 x + 1}{4}

二次equationの解:

y = - \frac{- x + x ^{2} + x x ^{2} + 6 x + 1}{4}, y = - \frac{- x + x ^{2} - x x ^{2} + 6 x + 1}{4}

グラフ

人気の例

60 x^{2} = 0

12 - 12 x^{2} = 0

x^{2} + 32 = 25

x^{2} - 34 x + 264 = 0

- (x - 1)^{2} = 0