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受欢迎的代数 >

solvefor y,x^3(x-y)^2=x^2-y^2

解答

求解

y, x^{3} (x - y)^{2} = x^{2} - y^{2}

解答

y = x, y = \frac{x ( x ^{3} - 1 )}{x ^{3} + 1}; x \neq = - 1, x \neq = \frac{1}{2} - \frac{3}{2} i, x \neq = \frac{1}{2} + \frac{3}{2} i

求解步骤

x^{3} (x - y)^{2} = x^{2} - y^{2}

展开

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

x^{5} - 2 y x^{4} + y^{2} x^{3} = x^{2} - y^{2}

将

y^{2}

para o lado esquerdo

x^{5} - 2 y x^{4} + y^{2} x^{3} + y^{2} = x^{2}

将

x^{2}

para o lado esquerdo

x^{5} - 2 y x^{4} + y^{2} x^{3} + y^{2} - x^{2} = 0

改写成标准形式

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

(x^{3} + 1) y^{2} - 2 x^{4} y + x^{5} - x^{2} = 0

使用求根公式求解

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

化简

(- 2 x^{4})^{2} - 4 (x^{3} + 1) (x^{5} - x^{2}) : 2 x

y_{1, 2} = \frac{- ( - 2 x ^{4} ) \pm 2 x}{2 ( x ^{3} + 1 )}; x \neq = - 1, x \neq = \frac{1}{2} - \frac{3}{2} i, x \neq = \frac{1}{2} + \frac{3}{2} i

将解分隔开

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

y = \frac{- ( - 2 x ^{4} ) + 2 x}{2 ( x ^{3} + 1 )} : x

y = \frac{- ( - 2 x ^{4} ) - 2 x}{2 ( x ^{3} + 1 )} : \frac{x ( x ^{3} - 1 )}{x ^{3} + 1}

二次方程组的解是:

y = x, y = \frac{x ( x ^{3} - 1 )}{x ^{3} + 1}; x \neq = - 1, x \neq = \frac{1}{2} - \frac{3}{2} i, x \neq = \frac{1}{2} + \frac{3}{2} i

作图

流行的例子

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s im pl i f y (2 x)^{\frac{4}{5}}

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f a c t or x^{2} + 3 x - 10

14 - 6 u \leq 2 - 9 u

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(y - 3)^{2} = 3 y - 5