[tex]\it{\overline{ab} +\overline{ba} =10a+b+10b+a=11a+11b = 11(a+b)}[/tex]
[tex]\overline{ab} + \overline{ba} \ este\ patrat\ perfect \Longrightarrow 11(a+b)
\ este\ patrat\ perfect
Deci, \ a+b = 11\ \ \ \ (1)[/tex]
[tex]\it{\overline{ab} -\overline{ba} =10a+b-10b-a=9a-9b =9(a-b)}[/tex]
[tex]\overline{ab} - \overline{ba}\ e \ patrat \ perfect \Longrightarrow 9(a-b) \ e \ patrat \ perfect[/tex]
Singura varianta convenabila este a - b = 1 (2)
Din relatiile (1), (2), rezulta a = 6, b = 5.
