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Inequality x^2y+y^2z+z^2x \geq 2(x+y+z)-3 [PAMO 2017, P2]

Source: Pan African Mathematical Olympiad 2017, Problem 2

July 5, 2017
algebraic inequalityPAMOinequalities

Problem Statement

Let x,yx,y, and zz be positive real numbers such that xy+yz+zx=3xyzxy+yz+zx=3xyz. Prove that x2y+y2z+z2x≥2(x+y+z)−3.x^2y+y^2z+z^2x \geq 2(x+y+z)-3. In which cases do we have equality?
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