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受欢迎的代数 >

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

解答

求解

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

解答

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}

求解步骤

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

在两边乘以

2

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

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

展开

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

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

两边减去

2 x f + 2 xg

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

化简

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

使用求根公式求解

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

化简

(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}

将解分隔开

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}

二次方程组的解是:

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}

作图

流行的例子

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