Question

determinati toate numerele naturale ab numar cu proprietatea 7×a+2×b=40 rapiidd​

Answer 1

$\it n=\overline{ab} \Longrightarrow a\ne0\ \ \ \ (1)\\ \\ 7a+2b=40 \Longrightarrow 7a=40-2b\ \ \ \ (2)\\ \\ 40-2b\in M_2\stackrel{(2)}{\Longrightarrow }\ a\in M_2\ \ \ \ (3) \\ \\ (2) \Longrightarrow 7a<40 \Longrightarrow a<6\ \ \ \ (4)\\ \\ (1),\ (3),\ (4) \Longrightarrow a\in\{2,\ 4\}$

$\it a=2\stackrel{(2)}{\Longrightarrow } 7\cdot2=40-2b \Longrightarrow 14=40-2b\Longrightarrow 2b=40-14 \Longrightarrow \\ \\ \Longrightarrow 2b=26|_{;2}\Longrightarrow b=13\ (nu\ convine,\ nu\ este\ cifr\breve{a})\\ \\ a=4\stackrel{(2)}{\Longrightarrow } 7\cdot4=40-2b \Longrightarrow 28=40-2b\Longrightarrow 2b=40-28 \Longrightarrow \\ \\ \Longrightarrow 2b=12|_{;2}\Longrightarrow b=6$

a=4,  b = 6 ⇒ n = 46.