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Bosnia and Herzegovina JBMO TST 2012 Problem 4

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2012

September 16, 2018

TriangleperimeterInequalitygeometryinequalities

Problem Statement

a

b

and

c

are sides of triangle which perimeter equals

1

, prove that:

a^2+b^2+c^2+4abc<\frac{1}{2}