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受欢迎的代数 >

(x^2+3x)(m+1)=(5x+12)(m-1)

解答

(x^{2} + 3 x) (m + 1) = (5 x + 12) (m - 1)

解答

x = \frac{m - 4 + 13 m ^{2} - 8 m + 4}{m + 1}, x = \frac{m - 4 - 13 m ^{2} - 8 m + 4}{m + 1}; m \neq = - 1

求解步骤

(x^{2} + 3 x) (m + 1) = (5 x + 12) (m - 1)

展开

(x^{2} + 3 x) (m + 1) : m x^{2} + x^{2} + 3 m x + 3 x

展开

(5 x + 12) (m - 1) : 5 m x - 5 x + 12 m - 12

m x^{2} + x^{2} + 3 m x + 3 x = 5 m x - 5 x + 12 m - 12

将

12

para o lado esquerdo

m x^{2} + x^{2} + 3 m x + 3 x + 12 = 5 m x - 5 x + 12 m

将

12 m

para o lado esquerdo

m x^{2} + x^{2} + 3 m x + 3 x + 12 - 12 m = 5 m x - 5 x

将

5 x

para o lado esquerdo

m x^{2} + x^{2} + 3 m x + 8 x - 12 m + 12 = 5 m x

将

5 m x

para o lado esquerdo

m x^{2} + x^{2} - 2 m x + 8 x - 12 m + 12 = 0

改写成标准形式

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

(m + 1) x^{2} + (- 2 m + 8) x - 12 m + 12 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 2 m + 8 ) \pm ( - 2 m + 8 ) ^{2} - 4 ( m + 1 ) ( - 12 m + 12 )}{2 ( m + 1 )}

化简

(- 2 m + 8)^{2} - 4 (m + 1) (- 12 m + 12) : 2 13 m^{2} - 8 m + 4

x_{1, 2} = \frac{- ( - 2 m + 8 ) \pm 2 13 m ^{2} - 8 m + 4}{2 ( m + 1 )}; m \neq = - 1

将解分隔开

x_{1} = \frac{- ( - 2 m + 8 ) + 2 13 m ^{2} - 8 m + 4}{2 ( m + 1 )}, x_{2} = \frac{- ( - 2 m + 8 ) - 2 13 m ^{2} - 8 m + 4}{2 ( m + 1 )}

x = \frac{- ( - 2 m + 8 ) + 2 13 m ^{2} - 8 m + 4}{2 ( m + 1 )} : \frac{m - 4 + 13 m ^{2} - 8 m + 4}{m + 1}

x = \frac{- ( - 2 m + 8 ) - 2 13 m ^{2} - 8 m + 4}{2 ( m + 1 )} : \frac{m - 4 - 13 m ^{2} - 8 m + 4}{m + 1}

二次方程组的解是:

x = \frac{m - 4 + 13 m ^{2} - 8 m + 4}{m + 1}, x = \frac{m - 4 - 13 m ^{2} - 8 m + 4}{m + 1}; m \neq = - 1

作图

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