Question

aflati numerele a si b pentru care 3^a + 4b = ab​

Answer 1

$\displaystyle\it\\3^a+4b=\overline{ab},~observam~ca~10\leq \overline{ab}\leq 99 \implies\\10 \leq 3^a+4b\leq 99 \implies 1 \leq a\leq 4,~a\in\mathbb{N}.\\3^a+4b=\overline{ab}=10a+b \implies 3^a+3b=10a\implies \\10a-3^a=\mathcal{M}_3,~dar,~10a-3a=10a-\mathcal{M}_3 \implies 10a=\mathcal{M}_3 \implies \\a=\mathcal{M}_3,~dar,~1\leq a\leq 4 \implies \boxed{\it a=3} \implies \boxed{\it b=1}~.$