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受欢迎的代数 >

solvefor y,z=x^3-2y^2+2xy

解答

求解

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

解答

y = - \frac{- x + x ^{2} + 2 ( x ^{3} - z )}{2}, y = \frac{x + x ^{2} + 2 ( x ^{3} - z )}{2}

求解步骤

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

交换两边

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

将

z

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

y = \frac{- 2 x + 2 x ^{2} + 2 ( x ^{3} - z )}{2 ( - 2 )} : - \frac{- x + x ^{2} + 2 ( x ^{3} - z )}{2}

y = \frac{- 2 x - 2 x ^{2} + 2 ( x ^{3} - z )}{2 ( - 2 )} : \frac{x + x ^{2} + 2 ( x ^{3} - z )}{2}

二次方程组的解是:

y = - \frac{- x + x ^{2} + 2 ( x ^{3} - z )}{2}, y = \frac{x + x ^{2} + 2 ( x ^{3} - z )}{2}

作图

流行的例子

a x^{2} + 4 x - a x - 4 = 0

\frac{4 x ^{2} - 9 x}{3} = 0

0 = x^{2} - 10 x + 24

5(x+4)^2=2(x+1)^2-27

5 (x + 4)^{2} = 2 (x + 1)^{2} - 27

x^2-100x+2500=1152pi^2x-56700pi^2

x^{2} - 100 x + 2500 = 1152 π^{2} x - 56700 π^{2}