Question

[x(x + 1)]/4 – (x – 5)/12=5(2x – 1)/6

alguém se dispõe?

Answer 1

$\dfrac{x(x+1)}{4}-\dfrac{(x-5)}{12}=\dfrac{5(2x-1)}{6}$

O mmc é 12

$3x(x+1)-(x-5)=2\cdot5(2x-1)$
$3x^2+3x-x+5=20x-10$
$3x^2-18x+15=0$

Simplificando por $3$:

$x^2-6x+5=0$
$\Delta=(-6)^2-4\cdot1\cdot5$
$\Delta=36-20$
$\Delta=16$

$x=\dfrac{-(-6)\pm\sqrt{16}}{2\cdot1}=\dfrac{6\pm4}{2}=3\pm2$

$x'=3+2~\longrightarrow~\boxed{x'=5}$

$x"=3-2~\longrightarrow~\boxed{x"=1}$

$\text{S}=\{1,5\}$