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受欢迎的代数 >

solvefor y,2xy+x^3-3y^2=5

解答

求解

y, 2 x y + x^{3} - 3 y^{2} = 5

解答

y = - \frac{- x + x ^{2} + 3 ( x ^{3} - 5 )}{3}, y = \frac{x + x ^{2} + 3 ( x ^{3} - 5 )}{3}

求解步骤

2 x y + x^{3} - 3 y^{2} = 5

将

5

para o lado esquerdo

2 x y + x^{3} - 3 y^{2} - 5 = 0

改写成标准形式

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

- 3 y^{2} + 2 x y + x^{3} - 5 = 0

使用求根公式求解

y_{1, 2} = \frac{- 2 x \pm ( 2 x ) ^{2} - 4 ( - 3 ) ( x ^{3} - 5 )}{2 ( - 3 )}

化简

(2 x)^{2} - 4 (- 3) (x^{3} - 5) : 2 x^{2} + 3 (x^{3} - 5)

y_{1, 2} = \frac{- 2 x \pm 2 x ^{2} + 3 ( x ^{3} - 5 )}{2 ( - 3 )}

将解分隔开

y_{1} = \frac{- 2 x + 2 x ^{2} + 3 ( x ^{3} - 5 )}{2 ( - 3 )}, y_{2} = \frac{- 2 x - 2 x ^{2} + 3 ( x ^{3} - 5 )}{2 ( - 3 )}

y = \frac{- 2 x + 2 x ^{2} + 3 ( x ^{3} - 5 )}{2 ( - 3 )} : - \frac{- x + x ^{2} + 3 ( x ^{3} - 5 )}{3}

y = \frac{- 2 x - 2 x ^{2} + 3 ( x ^{3} - 5 )}{2 ( - 3 )} : \frac{x + x ^{2} + 3 ( x ^{3} - 5 )}{3}

二次方程组的解是:

y = - \frac{- x + x ^{2} + 3 ( x ^{3} - 5 )}{3}, y = \frac{x + x ^{2} + 3 ( x ^{3} - 5 )}{3}

作图

流行的例子

y^{2} + 10 y + 24 = 0

((x+3)^2)/(81)-((x-4)^2)/(16)=1

\frac{( x + 3 ) ^{2}}{81} - \frac{( x - 4 ) ^{2}}{16} = 1

3 x - 17 + 3 x^{2} = - 4

3 x^{2} - 2 = 5 x

3 x^{2} - 432 = 0