IMO Shortlist 2001 problem N2
Dodao/la:
arhiva2. travnja 2012. Consider the system
![x + y = z + u](/media/m/e/1/d/e1da566d360dadd1465d7c223fc793b9.png)
,
![2xy = zu](/media/m/6/7/6/676235b953fad45db9919a6a37053f9e.png)
. Find the greatest value of the real constant
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
such that
![m \leq x/y](/media/m/e/1/c/e1cd52138e58979b4503a2ccecbc2955.png)
for any positive integer solution
![(x,y,z,u)](/media/m/7/1/0/710c2661ea84b29f263a59f813c0f53f.png)
of the system, with
![x \geq y](/media/m/4/c/f/4cf15742197dfe4cb55aac6dfcd77ba2.png)
.
%V0
Consider the system $x + y = z + u$, $2xy = zu$. Find the greatest value of the real constant $m$ such that $m \leq x/y$ for any positive integer solution $(x,y,z,u)$ of the system, with $x \geq y$.
Izvor: Međunarodna matematička olimpijada, shortlist 2001