IMO Shortlist 2005 problem A5
Dodao/la:
arhiva2. travnja 2012. Let
![x,y,z](/media/m/b/7/2/b72c022e9d438802d328d34eb61bb4ba.png)
be three positive reals such that
![xyz\geq 1](/media/m/2/0/9/209af82bcedf0a59ce4d94a011118370.png)
. Prove that
Hojoo Lee, Korea
%V0
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