[tex]\overline{ab}=10a+b\\
\overline{ba}=10b+a\\
\overline{ab}+\overline{ba}=10a+b+10b+a=11a+11b=11(a+b)\\
\text{Pentru ca $11(a+b)$ sa fie patrat perfect, tinand seama ca $a+b\leq18$}\\
\text{este necesar si suficient ca $a+b=11$.}\\
\text{Asadar, obtinem numerele care indeplinesc conditia data: }\\
29,38,47,56,65,74,83,92. [/tex]
