ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

x^3-3x-2=(x-a)^2(x+b)

解

x^{3} - 3 x - 2 = (x - a)^{2} (x + b)

解

x = \frac{- a ^{2} + 2 ab - 3 + a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}, x = \frac{- a ^{2} + 2 ab - 3 - a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}; - 2 a + b \neq = 0

解答ステップ

x^{3} - 3 x - 2 = (x - a)^{2} (x + b)

拡張

(x - a)^{2} (x + b) : x^{3} + b x^{2} - 2 a x^{2} - 2 ab x + a^{2} x + a^{2} b

x^{3} - 3 x - 2 = x^{3} + b x^{2} - 2 a x^{2} - 2 ab x + a^{2} x + a^{2} b

辺を交換する

x^{3} + b x^{2} - 2 a x^{2} - 2 ab x + a^{2} x + a^{2} b = x^{3} - 3 x - 2

2

を左側に移動します

x^{3} + b x^{2} - 2 a x^{2} - 2 ab x + a^{2} x + a^{2} b + 2 = x^{3} - 3 x

3 x

を左側に移動します

x^{3} + b x^{2} - 2 a x^{2} - 2 ab x + a^{2} x + a^{2} b + 2 + 3 x = x^{3}

x^{3}

を左側に移動します

- 2 a x^{2} + b x^{2} + a^{2} x - 2 ab x + 3 x + a^{2} b + 2 = 0

標準的な形式で書く

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

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

解くとthe二次式

x_{1, 2} = \frac{- ( a ^{2} - 2 ab + 3 ) \pm ( a ^{2} - 2 ab + 3 ) ^{2} - 4 ( - 2 a + b ) ( a ^{2} b + 2 )}{2 ( - 2 a + b )}

簡素化

(a^{2} - 2 ab + 3)^{2} - 4 (- 2 a + b) (a^{2} b + 2) : a^{4} + 4 a^{3} b + 6 a^{2} - 12 ab + 16 a - 8 b + 9

x_{1, 2} = \frac{- ( a ^{2} - 2 ab + 3 ) \pm a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}; - 2 a + b \neq = 0

解を分離する

x_{1} = \frac{- ( a ^{2} - 2 ab + 3 ) + a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}, x_{2} = \frac{- ( a ^{2} - 2 ab + 3 ) - a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}

x = \frac{- ( a ^{2} - 2 ab + 3 ) + a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )} : \frac{- a ^{2} + 2 ab - 3 + a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}

x = \frac{- ( a ^{2} - 2 ab + 3 ) - a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )} : \frac{- a ^{2} + 2 ab - 3 - a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}

二次equationの解:

x = \frac{- a ^{2} + 2 ab - 3 + a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}, x = \frac{- a ^{2} + 2 ab - 3 - a ^{4} + 4 a ^{3} b + 6 a ^{2} - 12 ab + 16 a - 8 b + 9}{2 ( - 2 a + b )}; - 2 a + b \neq = 0

グラフ

人気の例

x^2-1=0,y^2+z=0,z^2+y=0

x^{2} - 1 = 0, y^{2} + z = 0, z^{2} + y = 0

(x+3)(x-2)=4(x-2)

(x + 3) (x - 2) = 4 (x - 2)

(x + 9)^{2} = 24

11 = x^{2} + x - 1

5x^2-3x=x^2-4x+7

5 x^{2} - 3 x = x^{2} - 4 x + 7