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受欢迎的代数 >

solvefor x,f(x+2)=3x^2+2x-4

解答

求解

x, f (x + 2) = 3 x^{2} + 2 x - 4

解答

x = \frac{- 2 + f + f ^{2} + 20 f + 52}{6}, x = \frac{- 2 + f - f ^{2} + 20 f + 52}{6}

求解步骤

f (x + 2) = 3 x^{2} + 2 x - 4

展开

f (x + 2) : x f + 2 f

x f + 2 f = 3 x^{2} + 2 x - 4

交换两边

3 x^{2} + 2 x - 4 = x f + 2 f

将

2 f

para o lado esquerdo

3 x^{2} + 2 x - 4 - 2 f = x f

将

x f

para o lado esquerdo

3 x^{2} + 2 x - 4 - 2 f - x f = 0

改写成标准形式

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

3 x^{2} + (2 - f) x - 4 - 2 f = 0

使用求根公式求解

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

化简

(2 - f)^{2} - 4 \cdot 3 (- 4 - 2 f) : f^{2} + 20 f + 52

x_{1, 2} = \frac{- ( 2 - f ) \pm f ^{2} + 20 f + 52}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( 2 - f ) + f ^{2} + 20 f + 52}{2 \cdot 3}, x_{2} = \frac{- ( 2 - f ) - f ^{2} + 20 f + 52}{2 \cdot 3}

x = \frac{- ( 2 - f ) + f ^{2} + 20 f + 52}{2 \cdot 3} : \frac{- 2 + f + f ^{2} + 20 f + 52}{6}

x = \frac{- ( 2 - f ) - f ^{2} + 20 f + 52}{2 \cdot 3} : \frac{- 2 + f - f ^{2} + 20 f + 52}{6}

二次方程组的解是:

x = \frac{- 2 + f + f ^{2} + 20 f + 52}{6}, x = \frac{- 2 + f - f ^{2} + 20 f + 52}{6}

作图

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