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受欢迎的代数 >

solvefor y,f=13-x^3-y^2-z^2-12xy-2z

解答

求解

y, f = 13 - x^{3} - y^{2} - z^{2} - 12 x y - 2 z

解答

y = - 6 x - - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f, y = - 6 x + - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f

求解步骤

f = 13 - x^{3} - y^{2} - z^{2} - 12 x y - 2 z

交换两边

13 - x^{3} - y^{2} - z^{2} - 12 x y - 2 z = f

将

f

para o lado esquerdo

13 - x^{3} - y^{2} - z^{2} - 12 x y - 2 z - f = 0

改写成标准形式

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

- y^{2} - 12 x y + 13 - x^{3} - z^{2} - 2 z - f = 0

使用求根公式求解

y_{1, 2} = \frac{- ( - 12 x ) \pm ( - 12 x ) ^{2} - 4 ( - 1 ) ( 13 - x ^{3} - z ^{2} - 2 z - f )}{2 ( - 1 )}

化简

(- 12 x)^{2} - 4 (- 1) (13 - x^{3} - z^{2} - 2 z - f) : 2 36 x^{2} - x^{3} - z^{2} + 13 - f - 2 z

y_{1, 2} = \frac{- ( - 12 x ) \pm 2 36 x ^{2} - x ^{3} - z ^{2} + 13 - f - 2 z}{2 ( - 1 )}

将解分隔开

y_{1} = \frac{- ( - 12 x ) + 2 36 x ^{2} - x ^{3} - z ^{2} + 13 - f - 2 z}{2 ( - 1 )}, y_{2} = \frac{- ( - 12 x ) - 2 36 x ^{2} - x ^{3} - z ^{2} + 13 - f - 2 z}{2 ( - 1 )}

y = \frac{- ( - 12 x ) + 2 36 x ^{2} - x ^{3} - z ^{2} + 13 - f - 2 z}{2 ( - 1 )} : - 6 x - - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f

y = \frac{- ( - 12 x ) - 2 36 x ^{2} - x ^{3} - z ^{2} + 13 - f - 2 z}{2 ( - 1 )} : - 6 x + - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f

二次方程组的解是:

y = - 6 x - - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f, y = - 6 x + - x^{3} + 36 x^{2} + 13 - z^{2} - 2 z - f

作图

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