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受欢迎的代数 >

solvefor x,f(x+2)=-x^2+4x+1

解答

求解

x, f (x + 2) = - x^{2} + 4 x + 1

解答

x = - \frac{- 4 + f + f ^{2} - 16 f + 20}{2}, x = - \frac{- 4 + f - f ^{2} - 16 f + 20}{2}

求解步骤

f (x + 2) = - x^{2} + 4 x + 1

展开

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

x f + 2 f = - x^{2} + 4 x + 1

交换两边

- x^{2} + 4 x + 1 = x f + 2 f

将

2 f

para o lado esquerdo

- x^{2} + 4 x + 1 - 2 f = x f

将

x f

para o lado esquerdo

- x^{2} + 4 x + 1 - 2 f - x f = 0

改写成标准形式

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

- x^{2} + (4 - f) x + 1 - 2 f = 0

使用求根公式求解

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

化简

(4 - f)^{2} - 4 (- 1) (1 - 2 f) : f^{2} - 16 f + 20

x_{1, 2} = \frac{- ( 4 - f ) \pm f ^{2} - 16 f + 20}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- ( 4 - f ) + f ^{2} - 16 f + 20}{2 ( - 1 )}, x_{2} = \frac{- ( 4 - f ) - f ^{2} - 16 f + 20}{2 ( - 1 )}

x = \frac{- ( 4 - f ) + f ^{2} - 16 f + 20}{2 ( - 1 )} : - \frac{- 4 + f + f ^{2} - 16 f + 20}{2}

x = \frac{- ( 4 - f ) - f ^{2} - 16 f + 20}{2 ( - 1 )} : - \frac{- 4 + f - f ^{2} - 16 f + 20}{2}

二次方程组的解是:

x = - \frac{- 4 + f + f ^{2} - 16 f + 20}{2}, x = - \frac{- 4 + f - f ^{2} - 16 f + 20}{2}

作图

流行的例子

x (3 x - 7) = - 4

9 z^{2} - 3 z = 20

2 (x + 3)^{2} = 9

4 r^{2} + 3 r + 6 = 357

144 x^{2} - 9 = 0