Problem
ALG-B1-M12-P031 Variant 8, Problem 3
#31
★★★★★ Level 5 of 5
Let \(x,y,z>0\). Prove \(\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}\ge\frac{x+y+z}{2}\).
Cauchy.
By Cauchy, the left side is at least \(\frac{(x+y+z)^2}{2(x+y+z)}\).
Mock olympiad problem. Tags: inequality.