[tex]\overline{ab} = 10 \cdot a + b[/tex]
[tex]\overline{ba} = 10 \cdot b + a[/tex]
[tex]\overline{ab} + \overline{ba} = 10 \cdot a + b + 10 \cdot b + a[/tex]
[tex]\overline{ab} + \overline{ba} = 11 (a+b) [/tex]
Dar, [tex]\overline{ab} + \overline{ba} = 121[/tex], deci:
121 = 11 (a+b)
a + b = 121 : 11
a + b = 11
Stim ca 0 < a < b < 10, deci sunt doar cateva posibilitati:
1. a = 2, b = 9
2. a = 3, b = 8
3. a = 4, b = 7
4. a = 5, b = 6
