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受欢迎的代数 >

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

解答

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

解答

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

求解步骤

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

展开

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

展开

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

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

交换两边

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

将

a x

para o lado esquerdo

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

将

b x

para o lado esquerdo

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

将

x^{2}

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

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

作图

流行的例子

- 8 x^{2} = - 800

x^{2} + 5 x = - 3

- x^{2} + 18 x - 81 = 0

((x-3)^2)/(25)=0

\frac{( x - 3 ) ^{2}}{25} = 0

t^{2} + 30 t = - 17