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Symmetric inequality with two directions

Source: Germany 2017, Problem 5

May 4, 2017
inequalitiesinequalities proposedSymmetric inequalityGermany

Problem Statement

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}.
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