RMO 2014 M1

Mumbai Region

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

Dataset text AI-MO AoPS. Quoted with source.

Official text: Indian Regional Mathematical Olympiad 2014 official paper, page 1.

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