\(\left\{{}\begin{matrix}\overline{7ab}⋮9\\a-b=3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}7+a+b⋮9\\a-b=3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b\in\left\{2;11\right\}\\a-b=3\end{matrix}\right.\)
mà \(\left\{{}\begin{matrix}a+b=2\\a-b=3\end{matrix}\right.\) (vô lí)
\(\Rightarrow\left\{{}\begin{matrix}a+b=11\\a-b=3\end{matrix}\right.\)
\(\Rightarrow a=\left(11+3\right):2=7\Rightarrow b=11-7=4\)
Vậy \(\left\{{}\begin{matrix}a=7\\b=4\end{matrix}\right.\) thỏa mãn đề bài
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