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Ineq x^2 + y^2 + z^2 = 1 implies x^2yz + xy^2z + xyz^2 ≤ 1/3

Source: XII Rioplatense Mathematical Olympiad (2003), Level 3

August 8, 2011
inequalitiesinequalities unsolved

Problem Statement

Let xx, yy, and zz be positive real numbers satisfying x2+y2+z2=1x^2+y^2+z^2=1. Prove that x2yz+xy2z+xyz2≤13.x^2yz+xy^2z+xyz^2\le\frac{1}{3}.
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