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受欢迎的代数 >

(2x+4)(3x+6)=a(x^2+bx+c)

解答

(2 x + 4) (3 x + 6) = a (x^{2} + b x + c)

解答

x = \frac{- 24 + ab + a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}, x = \frac{- 24 + ab - a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}; a \neq = 6

求解步骤

(2 x + 4) (3 x + 6) = a (x^{2} + b x + c)

展开

(2 x + 4) (3 x + 6) : 6 x^{2} + 24 x + 24

展开

a (x^{2} + b x + c) : a x^{2} + ab x + a c

6 x^{2} + 24 x + 24 = a x^{2} + ab x + a c

两边减去

ab x + a c

6 x^{2} + 24 x + 24 - (ab x + a c) = a x^{2} + ab x + a c - (ab x + a c)

化简

6 x^{2} + 24 x + 24 - ab x - a c = a x^{2}

将

a x^{2}

para o lado esquerdo

6 x^{2} + 24 x + 24 - ab x - a c - a x^{2} = 0

改写成标准形式

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

(6 - a) x^{2} + (24 - ab) x + 24 - a c = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 24 - ab ) \pm ( 24 - ab ) ^{2} - 4 ( 6 - a ) ( 24 - a c )}{2 ( 6 - a )}

化简

(24 - ab)^{2} - 4 (6 - a) (24 - a c) : a^{2} b^{2} - 4 a^{2} c + 24 a c + 96 a - 48 ab

x_{1, 2} = \frac{- ( 24 - ab ) \pm a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}; a \neq = 6

将解分隔开

x_{1} = \frac{- ( 24 - ab ) + a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}, x_{2} = \frac{- ( 24 - ab ) - a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}

x = \frac{- ( 24 - ab ) + a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )} : \frac{- 24 + ab + a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}

x = \frac{- ( 24 - ab ) - a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )} : \frac{- 24 + ab - a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}

二次方程组的解是:

x = \frac{- 24 + ab + a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}, x = \frac{- 24 + ab - a ^{2} b ^{2} - 4 a ^{2} c + 24 a c + 96 a - 48 ab}{2 ( 6 - a )}; a \neq = 6

作图

流行的例子

x^{2} - 2 \cdot x - 3 = 0

4 (x + 1)^{2} = 18

x^{2} - 12 x - 81 = - 9

7 x^{2} = 2 x + 6

x^2-8x+32=12x-4

x^{2} - 8 x + 32 = 12 x - 4