Question

como resolve
x/q + x + x*q= 39 Isso e PG o x e 9 como fica

Answer 1

$\dfrac{x}{q}+x+xq=39\\\\ \dfrac{9}{q}+9+9q=39\\\\ \dfrac{9}{q}+9q=30\\\\ 9+9q^2=30q\\\\ 3+3q^2=10q\\\\ 3q^2-10q+3=0\\\\ \Delta=b^2-4\cdot a\cdot c\\ \Delta=(-10)-4\cdot3\cdot3\\ \Delta=100-36\\ \Delta=64\\\\ q=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{10\pm\sqrt{64}}{2\cdot3}=\dfrac{10\pm8}{6}=\dfrac{5\pm4}{3}\Lonrightarrow\begin{cases}q_1=\frac{9}{3}=3\\q_2=\frac{1}{3}\end{cases}$


$S=\{\dfrac{1}{3},3\}$