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人気のある代数 >

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

解

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

解

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

解答ステップ

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

拡張

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

拡張

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

両辺から

ab x + a c

を引く

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

簡素化

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

a x^{2}

を左側に移動します

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

標準的な形式で書く

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

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

解くとthe二次式

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

簡素化

(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

解を分離する

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equationの解:

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

グラフ

人気の例

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