Question

Determinați numarul natural ab stiind ca ab-3a-3b=4
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Answer 1

$\it \overline{ab}-3a-3b=4 \Rightarrow 10a+b-3a-3b=4 \Rightarrow 7a-2b=4 \Rightarrow \\ \\ \Rightarrow 7a=4+2b\ \ \ \ (1)\\ \\ (1) \Rightarrow a=cifr\breve{a}\ par\breve{a}\ nenul\breve{a}\ \ \ \ (2)\\ \\ b<10|_{\cdot2} \Rightarrow 2b<20|_{+4} \Rightarrow 4+2b<24 \stackrel{(1)}{\Longrightarrow} 7a<24\ \ \ \ \ (3)\\ \\ (2),\ (3) \Rightarrow a=2\ \ \ \ \ (4)$

$\it (1),\ (4) \Rightarrow 7\cdot2=4+2b \Rightarrow 14=4+2b|_{-4} \Rightarrow 10=2b \Rightarrow b=5\\ \\ Deci,\ \ \overline{ab}=25$