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xy+yz+xz=3xyz

Source: Balkan Mathematics Olympiad 2014 - Problem-1

May 4, 2014
algebrainequalitiesBalkan Mathematics Olympiad

Problem Statement

Let x,yx,y and zz be positive real numbers such that xy+yz+xz=3xyzxy+yz+xz=3xyz. Prove that x2y+y2z+z2x≥2(x+y+z)−3 x^2y+y^2z+z^2x \ge 2(x+y+z)-3 and determine when equality holds.
UK - David Monk
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