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人気のある代数 >

solvefor x, x/2-3+3x^2+x-6=(f+g)(x)

解

解く

x, \frac{x}{2} - 3 + 3 x^{2} + x - 6 = (f + g) (x)

解

x = \frac{- 3 + 2 f + 2 g + 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}, x = \frac{- 3 + 2 f + 2 g - 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}

解答ステップ

\frac{x}{2} - 3 + 3 x^{2} + x - 6 = (f + g) (x)

以下で両辺を乗じる:

2

x - 6 + 6 x^{2} + 2 x - 12 = 2 x (f + g)

6 x^{2} + 3 x - 18 = 2 x (f + g)

拡張

2 x (f + g) : 2 x f + 2 xg

6 x^{2} + 3 x - 18 = 2 x f + 2 xg

両辺から

2 x f + 2 xg

を引く

6 x^{2} + 3 x - 18 - (2 x f + 2 xg) = 2 x f + 2 xg - (2 x f + 2 xg)

簡素化

6 x^{2} + (3 - 2 f - 2 g) x - 18 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 3 - 2 f - 2 g ) \pm ( 3 - 2 f - 2 g ) ^{2} - 4 \cdot 6 ( - 18 )}{2 \cdot 6}

簡素化

(3 - 2 f - 2 g)^{2} - 4 \cdot 6 (- 18) : 4 f^{2} + 8 f g - 12 f + 4 g^{2} + 441 - 12 g

x_{1, 2} = \frac{- ( 3 - 2 f - 2 g ) \pm 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{2 \cdot 6}

解を分離する

x_{1} = \frac{- ( 3 - 2 f - 2 g ) + 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{2 \cdot 6}, x_{2} = \frac{- ( 3 - 2 f - 2 g ) - 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{2 \cdot 6}

x = \frac{- ( 3 - 2 f - 2 g ) + 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{2 \cdot 6} : \frac{- 3 + 2 f + 2 g + 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}

x = \frac{- ( 3 - 2 f - 2 g ) - 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{2 \cdot 6} : \frac{- 3 + 2 f + 2 g - 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}

二次equationの解:

x = \frac{- 3 + 2 f + 2 g + 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}, x = \frac{- 3 + 2 f + 2 g - 4 f ^{2} + 8 f g - 12 f + 4 g ^{2} + 441 - 12 g}{12}

グラフ

人気の例

solvefor x,x*y^2+x^2*y+1=0

so l v e f or x, x \cdot y^{2} + x^{2} \cdot y + 1 = 0

1.5 x^{2} + 2 x = 10

solvefor x,f=x^2-2x+k

so l v e f or x, f = x^{2} - 2 x + k

solvefor y,(d-y)^2+(d+y)^2=0

so l v e f or y, (d - y)^{2} + (d + y)^{2} = 0

solvefor x,x^2-6x-p^2-2p+8=0

so l v e f or x, x^{2} - 6 x - p^{2} - 2 p + 8 = 0