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z(xz+yz+y)/(xy+y^2+z^2+1) <= K

Source: Turkey TST 2013 - Day 2 - P3

April 2, 2013
inequalitiestrigonometryinequalities proposed

Problem Statement

For all real numbers x,y,zx,y,z such that −2≤x,y,z≤2-2\leq x,y,z \leq 2 and x2+y2+z2+xyz=4x^2+y^2+z^2+xyz = 4, determine the least real number KK satisfying z(xz+yz+y)xy+y2+z2+1≤K.\dfrac{z(xz+yz+y)}{xy+y^2+z^2+1} \leq K.
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