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Given a^2+5b^2+4c^2-4ab-4bc=0, can a,b,c form sides of Δ ?

Source: Mumbai Region RMO 2014 Problem 1

December 7, 2014
algebra proposedalgebra

Problem Statement

Three positive real numbers a,b,ca,b,c are such that a2+5b2+4c2−4ab−4bc=0a^2+5b^2+4c^2-4ab-4bc=0. Can a,b,ca,b,c be the lengths of te sides of a triangle? Justify your answer.
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