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4

Part of 2017 Bosnia and Herzegovina EGMO TST

Problems(1)

Bosnia and Herzegovina EGMO TST 2017 Problem 4

Source: Bosnia and Herzegovina EGMO Team Selection Test 2017

9/19/2018
Let aa, bb, cc, dd and ee be distinct positive real numbers such that a2+b2+c2+d2+e2=ab+ac+ad+ae+bc+bd+be+cd+ce+dea^2+b^2+c^2+d^2+e^2=ab+ac+ad+ae+bc+bd+be+cd+ce+de a)a) Prove that among these 55 numbers there exists triplet such that they cannot be sides of a triangle b)b) Prove that, for a)a), there exists at least 66 different triplets
tripletsequalityInequalityalgebra