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受欢迎的代数 >

solvefor Y,Y^2-Y=X^3-X

解答

求解

Y, Y^{2} - Y = X^{3} - X

解答

Y = \frac{1 + 1 - 4 ( X - X ^{3} )}{2}, Y = \frac{1 - 1 - 4 ( X - X ^{3} )}{2}

求解步骤

Y^{2} - Y = X^{3} - X

将

X

para o lado esquerdo

Y^{2} - Y + X = X^{3}

将

X^{3}

para o lado esquerdo

Y^{2} - Y + X - X^{3} = 0

使用求根公式求解

Y_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( X - X ^{3} )}{2 \cdot 1}

化简

(- 1)^{2} - 4 \cdot 1 \cdot (X - X^{3}) : 1 - 4 (X - X^{3})

Y_{1, 2} = \frac{- ( - 1 ) \pm 1 - 4 ( X - X ^{3} )}{2 \cdot 1}

将解分隔开

Y_{1} = \frac{- ( - 1 ) + 1 - 4 ( X - X ^{3} )}{2 \cdot 1}, Y_{2} = \frac{- ( - 1 ) - 1 - 4 ( X - X ^{3} )}{2 \cdot 1}

Y = \frac{- ( - 1 ) + 1 - 4 ( X - X ^{3} )}{2 \cdot 1} : \frac{1 + 1 - 4 ( X - X ^{3} )}{2}

Y = \frac{- ( - 1 ) - 1 - 4 ( X - X ^{3} )}{2 \cdot 1} : \frac{1 - 1 - 4 ( X - X ^{3} )}{2}

二次方程组的解是:

Y = \frac{1 + 1 - 4 ( X - X ^{3} )}{2}, Y = \frac{1 - 1 - 4 ( X - X ^{3} )}{2}

作图

流行的例子

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so l v e f or x, 6 x^{2} + 18 y^{2} + 36 y + 4 x + 56 = 0

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