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受欢迎的代数 >

a(x-a)+b(x-b)=x(x-a)+x(x-b)

解答

a (x - a) + b (x - b) = x (x - a) + x (x - b)

解答

x = \frac{a + b + - a ^{2} + 2 ab - b ^{2}}{2}, x = \frac{a + b - - a ^{2} + 2 ab - b ^{2}}{2}

求解步骤

a (x - a) + b (x - b) = x (x - a) + x (x - b)

展开

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

展开

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

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

交换两边

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

将

b^{2}

para o lado esquerdo

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

将

b x

para o lado esquerdo

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

将

a^{2}

para o lado esquerdo

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

将

a x

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(- 2 a - 2 b)^{2} - 4 \cdot 2 (a^{2} + b^{2}) : 2 - a^{2} + 2 ab - b^{2}

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

将解分隔开

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

x = \frac{- ( - 2 a - 2 b ) + 2 - a ^{2} + 2 ab - b ^{2}}{2 \cdot 2} : \frac{a + b + - a ^{2} + 2 ab - b ^{2}}{2}

x = \frac{- ( - 2 a - 2 b ) - 2 - a ^{2} + 2 ab - b ^{2}}{2 \cdot 2} : \frac{a + b - - a ^{2} + 2 ab - b ^{2}}{2}

二次方程组的解是:

x = \frac{a + b + - a ^{2} + 2 ab - b ^{2}}{2}, x = \frac{a + b - - a ^{2} + 2 ab - b ^{2}}{2}

作图

流行的例子

z^{2} + 2 z - 3 = 0

9 x^{2} - 25 x + 30 = 0

x^{2} + x = - 4 x^{2} + 16

x^{2} + 13 x + 43 = 11

0 = - 2 (x - 2)^{2} + 3