Question

(x/2+1) (x/2 – 1) – 5/4 =5x/8

Eu não consigo resollver...

Answer 1

$\left(\dfrac{x}{2}+1\right)\cdot\left(\dfrac{x}{2}-1\right)-\dfrac{5}{4}=\dfrac{5x}{8}$

Note que $\left(\dfrac{x}{2}+1\right)\cdot\left(\dfrac{x}{2}-1\right)$ é um produto notável.

Este aqui $(a+b)\cdot(a-b)=a^2-b^2$

Então $\left(\dfrac{x}{2}+1\right)\cdot\left(\dfrac{x}{2}-1\right)=\left(\dfrac{x}{2}\right)^2-1^2=\dfrac{x^2}{4}-1$

Substituindo:

$\dfrac{x^2}{4}-1-\dfrac{5}{4}=\dfrac{5x}{8}$

O mmc é 8

$2x^2-8-10=5x$
$2x^2-5x-18=0$

$\Delta=(-5)^2-4\cdot2\cdot(-18)$
$\Delta=25+144$
$\Delta=169$

$x=\dfrac{-(-5)\pm\sqrt{169}}{2\cdot2}=\dfrac{5\pm13}{4}$

$x'=\dfrac{5+13}{4}=\dfrac{18}{4}~\longrightarrow~\boxed{x'=\dfrac{9}{2}}$

$x"=\dfrac{5-13}{4}=\dfrac{-8}{4}~\longrightarrow~\boxed{x"=-2}$

$\text{S}=\{-2,\frac{9}{2}\}$