IMO Shortlist 1996 problem A1


Kvaliteta:
1
2
3
4
5
   Avg: 2,0
Težina:
1
2
3
4
5
6
7
8
9
10
   Avg: 4,7
Dodao/la: arhiva
2. travnja 2012.
1996 alg shortlist
LaTeX PDF
Suppose that a, b, c > 0 such that abc = 1. Prove that \frac{ab}{ab + a^5 + b^5} + \frac{bc}{bc + b^5 + c^5} + \frac{ca}{ca + c^5 + a^5} \leq 1.
Izvor: Međunarodna matematička olimpijada, shortlist 1996