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人気のある代数 >

solvefor y,2xy^2+4=2(3-x^2y)y

解

解く

y, 2 x y^{2} + 4 = 2 (3 - x^{2} y) y

解

y = \frac{3 + - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}, y = \frac{3 - - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}; x \neq = 0, x \neq = - 1

解答ステップ

2 x y^{2} + 4 = 2 (3 - x^{2} y) y

拡張

2 (3 - x^{2} y) y : 6 y - 2 y^{2} x^{2}

2 x y^{2} + 4 = 6 y - 2 y^{2} x^{2}

2 y^{2} x^{2}

を左側に移動します

2 x y^{2} + 4 + 2 y^{2} x^{2} = 6 y

6 y

を左側に移動します

2 x y^{2} + 4 + 2 y^{2} x^{2} - 6 y = 0

標準的な形式で書く

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

(2 x + 2 x^{2}) y^{2} - 6 y + 4 = 0

解くとthe二次式

y_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 ( 2 x + 2 x ^{2} ) \cdot 4}{2 ( 2 x + 2 x ^{2} )}

簡素化

(- 6)^{2} - 4 (2 x + 2 x^{2}) \cdot 4 : 2 9 - 8 x (x + 1)

y_{1, 2} = \frac{- ( - 6 ) \pm 2 9 - 8 x ( x + 1 )}{2 ( 2 x + 2 x ^{2} )}; x \neq = 0, x \neq = - 1

解を分離する

y_{1} = \frac{- ( - 6 ) + 2 9 - 8 x ( x + 1 )}{2 ( 2 x + 2 x ^{2} )}, y_{2} = \frac{- ( - 6 ) - 2 9 - 8 x ( x + 1 )}{2 ( 2 x + 2 x ^{2} )}

y = \frac{- ( - 6 ) + 2 9 - 8 x ( x + 1 )}{2 ( 2 x + 2 x ^{2} )} : \frac{3 + - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}

y = \frac{- ( - 6 ) - 2 9 - 8 x ( x + 1 )}{2 ( 2 x + 2 x ^{2} )} : \frac{3 - - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}

二次equationの解:

y = \frac{3 + - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}, y = \frac{3 - - 8 x ( x + 1 ) + 9}{2 x ( x + 1 )}; x \neq = 0, x \neq = - 1

グラフ

人気の例

-16t^2+80t+50=0

- 16 t^{2} + 80 t + 50 = 0

2 b^{2} + 4 b - 126 = 0

z^2+0.2z-0.08=0

z^{2} + 0.2 z - 0.08 = 0

因数 x^2=x+30

f a c t or x^{2} = x + 30

- 3 x^{2} + 15 = 0