[tex]Ecuatia~este~echivalenta~cu: \\ \\ \frac{ \overline{21a}}{90}+ \frac{\overline{2a1}}{90}= \frac{ \overline{a12}}{90}+ \frac{\overline{1a2}}{90} \Leftrightarrow \\ \\ \Leftrightarrow \overline{21a}+ \overline{2a1}= \overline{a12}+ \overline{1a2} \Leftrightarrow \\ \\ \Leftrightarrow 210+a+201+10a=100a+12+102+10a \Leftrightarrow \\ \\ \Leftrightarrow 210+201-12-102=100a+10a-a-10a \Leftrightarrow \\ \\ \Leftrightarrow 297=99a \Rightarrow \boxed{a=3}~. \\ \\ .[/tex]
