Problem
ALG-B1-M12-P015 Variant 4, Problem 3
#15
★★★☆☆ Level 3 of 5
Prove \(\frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}\ge\frac{x+y+z}{2}\) for \(x,y,z>0\).
Cauchy.
The left side is at least \(\frac{(x+y+z)^2}{2(x+y+z)}\).
Mock olympiad problem. Tags: cauchy.