IMO Shortlist 2005 problem A5


Kvaliteta:
  Avg: 4,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let x,y,z be three positive reals such that xyz\geq 1. Prove that
\frac { x^5-x^2 }{x^5+y^2+z^2} + \frac {y^5-y^2}{x^2+y^5+z^2} + \frac {z^5-z^2}{x^2+y^2+z^5} \geq 0 .
Hojoo Lee, Korea
Izvor: Međunarodna matematička olimpijada, shortlist 2005