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Inequality in positive integers!

Source: India TST 2001 Day 1 Problem 1

January 31, 2015
inequalitiesinequalities proposed

Problem Statement

Let xx , yy , z>0z>0. Prove that if xyz≥xy+yz+zxxyz\geq xy+yz+zx, then xyz≥3(x+y+z)xyz \geq 3(x+ y+z).
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