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受欢迎的代数 >

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

解答

求解

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

解答

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

求解步骤

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

展开

f (x - 3) : x f - 3 f

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

交换两边

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

将

3 f

para o lado esquerdo

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

将

x f

para o lado esquerdo

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

改写成标准形式

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

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

使用求根公式求解

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

化简

(- f)^{2} - 4 \cdot 1 \cdot (- 2 + 3 f) : f^{2} - 4 (- 2 + 3 f)

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

将解分隔开

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

x = \frac{- ( - f ) + f ^{2} - 4 ( - 2 + 3 f )}{2 \cdot 1} : \frac{f + f ^{2} - 4 ( - 2 + 3 f )}{2}

x = \frac{- ( - f ) - f ^{2} - 4 ( - 2 + 3 f )}{2 \cdot 1} : \frac{f - f ^{2} - 4 ( - 2 + 3 f )}{2}

二次方程组的解是:

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

作图

流行的例子

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

x^{2} - 11 x + 28 = 0, x

0=-16t^2+16t+64

0 = - 16 t^{2} + 16 t + 64

(x + 3) (2 x - 4) = 0

(y - 4)^{2} = - 100