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人気のある代数 >

solvefor y,z=yx^6-3x+8x^2y^2-y^2

解

解く

y, z = y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2}

解

y = \frac{- x ^{6} + x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}, y = \frac{- x ^{6} - x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}; x \neq = \frac{1}{2 2}, x \neq = - \frac{1}{2 2}

解答ステップ

z = y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2}

辺を交換する

y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2} = z

z

を左側に移動します

y x^{6} - 3 x + 8 x^{2} y^{2} - y^{2} - z = 0

標準的な形式で書く

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

(8 x^{2} - 1) y^{2} + x^{6} y - 3 x - z = 0

解くとthe二次式

y_{1, 2} = \frac{- x ^{6} \pm ( x ^{6} ) ^{2} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}

簡素化

(x^{6})^{2} - 4 (8 x^{2} - 1) (- 3 x - z) : x^{12} - 4 (8 x^{2} - 1) (- 3 x - z)

y_{1, 2} = \frac{- x ^{6} \pm x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}; x \neq = \frac{1}{2 2}, x \neq = - \frac{1}{2 2}

解を分離する

y_{1} = \frac{- x ^{6} + x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}, y_{2} = \frac{- x ^{6} - x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}

y = \frac{- x ^{6} + x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}; x \neq = \frac{1}{2 2}, x \neq = - \frac{1}{2 2}

y = \frac{- x ^{6} - x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}; x \neq = \frac{1}{2 2}, x \neq = - \frac{1}{2 2}

二次equationの解:

y = \frac{- x ^{6} + x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}, y = \frac{- x ^{6} - x ^{12} - 4 ( 8 x ^{2} - 1 ) ( - 3 x - z )}{2 ( 8 x ^{2} - 1 )}; x \neq = \frac{1}{2 2}, x \neq = - \frac{1}{2 2}

グラフ

人気の例

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