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受欢迎的代数 >

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

解答

求解

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

解答

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}

求解步骤

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

交换两边

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

将

z

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(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}

将解分隔开

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}

二次方程组的解是:

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}

作图

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