Question

det nr de forma ab astfel incat 3*ab +3*ba=165

Answer 1

3*ab+3*ba=165
<=> 3*(ab+ba)=165
<=> ab+ba=55
<=> 10a+b+10b+a=55
<=> 11a+11b=55
<=> 11(a+b)=55
<=> a+b=5.

Daca a=1 => b=4, deci ab=14
Daca a=2 => b=3, deci ab=23
Daca a=3 => b=2, deci ab=32
Daca a=4 => b=1, deci ab=41
Daca a=5 => b=0, deci ab=50

In concluzie, numerele de forma ab cu proprietatea din enunt sunt: 14, 23, 32, 41, 50.