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If a,b,c are sides of triangle then so are are <a^2+bct>

Source: European Girls’ Mathematical Olympiad-2014 - DAY 1 - P1

April 12, 2014
algebraEGMO

Problem Statement

Determine all real constants tt such that whenever aa, bb and cc are the lengths of sides of a triangle, then so are a2+bcta^2+bct, b2+catb^2+cat, c2+abtc^2+abt.
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