-4
$\begingroup$

Find all integers $a$ and $b$ such that $2a + 2b = ab$.

$\endgroup$
3
  • 1
    $\begingroup$ Welcome to MSE. What have you tried? Are you stuck on some concept? Please show your effort and give more details. Is this a homework problem? What level? $\endgroup$
    – Andrei
    May 27 '19 at 4:00
  • 1
    $\begingroup$ What have you tried? $\endgroup$
    – El Ectric
    May 27 '19 at 4:03
  • 5
    $\begingroup$ Hint: $2(a+b) = ab \iff (a-2)(b-2) = 4$. $\endgroup$ May 27 '19 at 4:04
6
$\begingroup$

$$\begin{align} 2a+2b &= ab \\ ab-2a-2b &= 0 \\ a(b-2)-2b &= 0 \\ a(b-2)-2b+4 &= 0+4 = 4 \\ a(b-2)-2(b-2) &= 4 \\ (a-2)(b-2) &= 4 \end{align}$$

Can you take it from here?

$\endgroup$
0

Not the answer you're looking for? Browse other questions tagged or ask your own question.