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受欢迎的代数 >

solvefor y,X+y=Xy(X-y)

解答

求解

y, X + y = X y (X - y)

解答

y = - \frac{- X ^{2} + 1 + X ^{4} - 6 X ^{2} + 1}{2 X}, y = - \frac{- X ^{2} + 1 - X ^{4} - 6 X ^{2} + 1}{2 X}; X \neq = 0

求解步骤

X + y = X y (X - y)

展开

X y (X - y) : y X^{2} - y^{2} X

X + y = y X^{2} - y^{2} X

交换两边

y X^{2} - y^{2} X = X + y

将

y

para o lado esquerdo

y X^{2} - y^{2} X - y = X

将

X

para o lado esquerdo

y X^{2} - y^{2} X - y - X = 0

改写成标准形式

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

- X y^{2} + (X^{2} - 1) y - X = 0

使用求根公式求解

y_{1, 2} = \frac{- ( X ^{2} - 1 ) \pm ( X ^{2} - 1 ) ^{2} - 4 ( - X ) ( - X )}{2 ( - X )}

化简

(X^{2} - 1)^{2} - 4 (- X) (- X) : X^{4} - 6 X^{2} + 1

y_{1, 2} = \frac{- ( X ^{2} - 1 ) \pm X ^{4} - 6 X ^{2} + 1}{2 ( - X )}; X \neq = 0

将解分隔开

y_{1} = \frac{- ( X ^{2} - 1 ) + X ^{4} - 6 X ^{2} + 1}{2 ( - X )}, y_{2} = \frac{- ( X ^{2} - 1 ) - X ^{4} - 6 X ^{2} + 1}{2 ( - X )}

y = \frac{- ( X ^{2} - 1 ) + X ^{4} - 6 X ^{2} + 1}{2 ( - X )} : - \frac{- X ^{2} + 1 + X ^{4} - 6 X ^{2} + 1}{2 X}

y = \frac{- ( X ^{2} - 1 ) - X ^{4} - 6 X ^{2} + 1}{2 ( - X )} : - \frac{- X ^{2} + 1 - X ^{4} - 6 X ^{2} + 1}{2 X}

二次方程组的解是:

y = - \frac{- X ^{2} + 1 + X ^{4} - 6 X ^{2} + 1}{2 X}, y = - \frac{- X ^{2} + 1 - X ^{4} - 6 X ^{2} + 1}{2 X}; X \neq = 0

作图

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