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An easy and classical inequality in 3 variables abc<=a+b+c

Source: Balkan MO 2001, problem 3

April 24, 2006
inequalitiesinequalities proposedalgebra

Problem Statement

Let aa, bb, cc be positive real numbers with abc≤a+b+cabc \leq a+b+c. Show that a2+b2+c2≥3abc. a^2 + b^2 + c^2 \geq \sqrt 3 abc. Cristinel Mortici, Romania
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