MathDB

5

Part of 2017 German National Olympiad

Problems(1)

Symmetric inequality with two directions

Source: Germany 2017, Problem 5

5/4/2017
Prove that for all non-negative numbers x,y,zx,y,z satisfying x+y+z=1x+y+z=1, one has 1≤x1−yz+y1−zx+z1−xy≤98.1 \le \frac{x}{1-yz}+\frac{y}{1-zx}+\frac{z}{1-xy} \le \frac{9}{8}.
inequalitiesinequalities proposedSymmetric inequalityGermany