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a + b + c >= \sqrt{\frac13 (a + 2)(b + 2)(c + 2)} when a,b,c>0 and abc=1

Source: Dutch IMO TST 2013 day 1 p5

August 29, 2019

algebrainequalitiesDutch MOHigh school olympiad

Problem Statement

Let

a, b

, and

c

be positive real numbers satisfying

abc = 1

. Show that

a + b + c \ge \sqrt{\frac13 (a + 2)(b + 2)(c + 2)}