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受欢迎的代数 >

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

解答

求解

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

解答

x = \frac{f + f ^{2} - 12 ( 2 - 2 f )}{6}, x = \frac{f - f ^{2} - 12 ( 2 - 2 f )}{6}

求解步骤

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

展开

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

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

交换两边

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

将

2 f

para o lado esquerdo

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

将

x f

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(- f)^{2} - 4 \cdot 3 (2 - 2 f) : f^{2} - 12 (2 - 2 f)

x_{1, 2} = \frac{- ( - f ) \pm f ^{2} - 12 ( 2 - 2 f )}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( - f ) + f ^{2} - 12 ( 2 - 2 f )}{2 \cdot 3}, x_{2} = \frac{- ( - f ) - f ^{2} - 12 ( 2 - 2 f )}{2 \cdot 3}

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

x = \frac{- ( - f ) - f ^{2} - 12 ( 2 - 2 f )}{2 \cdot 3} : \frac{f - f ^{2} - 12 ( 2 - 2 f )}{6}

二次方程组的解是:

x = \frac{f + f ^{2} - 12 ( 2 - 2 f )}{6}, x = \frac{f - f ^{2} - 12 ( 2 - 2 f )}{6}

作图

流行的例子

solvefor y,x-y^2=4

so l v e f or y, x - y^{2} = 4

x^{2} - 4 x + 130 = 14 x

p^{2} - 196 = 0

v^{2} = - 5 v - 4

solvefor x,f^{-1}(x)=x^2+1

so l v e f or x, f^{- 1} (x) = x^{2} + 1