Question

Fie a,b,c numere naturale nenule, astfel încat ab+ac+bc=abc . Calculați a+100\a+b+100\b+c+100\c.

Answer 1

ab+ac+bc=abc  l :abc
1/c+1/b+1/a=1 l x100
100/a+100/b+100/c=100 l +3
(100/a +1) +(100/b +1) +(100/c +1)=103
(a+100)/a +(b+100)/b +(c+100)/c=103