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受欢迎的代数 >

a^2(x-b)-b^2(x-a)=x^2(a-b)

解答

a^{2} \cdot (x - b) - b^{2} \cdot (x - a) = x^{2} (a - b)

解答

x = \frac{- b ^{2} + a ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}, x = \frac{- b ^{2} + a ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}; a - b \neq = 0

求解步骤

a^{2} (x - b) - b^{2} (x - a) = x^{2} (a - b)

展开

a^{2} (x - b) - b^{2} (x - a) : a^{2} x - a^{2} b - b^{2} x + a b^{2}

a^{2} x - a^{2} b - b^{2} x + a b^{2} = x^{2} (a - b)

交换两边

x^{2} (a - b) = a^{2} x - a^{2} b - b^{2} x + a b^{2}

两边减去

- b^{2} x + a b^{2}

x^{2} (a - b) - (- b^{2} x + a b^{2}) = a^{2} x - a^{2} b - b^{2} x + a b^{2} - (- b^{2} x + a b^{2})

化简

a x^{2} - b x^{2} + b^{2} x - a b^{2} = a^{2} x - a^{2} b

两边减去

a^{2} x - a^{2} b

a x^{2} - b x^{2} + b^{2} x - a b^{2} - (a^{2} x - a^{2} b) = a^{2} x - a^{2} b - (a^{2} x - a^{2} b)

化简

(a - b) x^{2} + (b^{2} - a^{2}) x - a b^{2} + a^{2} b = 0

使用求根公式求解

x_{1, 2} = \frac{- ( b ^{2} - a ^{2} ) \pm ( b ^{2} - a ^{2} ) ^{2} - 4 ( a - b ) ( - a b ^{2} + a ^{2} b )}{2 ( a - b )}

化简

(b^{2} - a^{2})^{2} - 4 (a - b) (- a b^{2} + a^{2} b) : a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}

x_{1, 2} = \frac{- ( b ^{2} - a ^{2} ) \pm a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}; a - b \neq = 0

将解分隔开

x_{1} = \frac{- ( b ^{2} - a ^{2} ) + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}, x_{2} = \frac{- ( b ^{2} - a ^{2} ) - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}

x = \frac{- ( b ^{2} - a ^{2} ) + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )} : \frac{- b ^{2} + a ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}

x = \frac{- ( b ^{2} - a ^{2} ) - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )} : \frac{- b ^{2} + a ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}

二次方程组的解是:

x = \frac{- b ^{2} + a ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}, x = \frac{- b ^{2} + a ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}; a - b \neq = 0

作图

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