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find k,l such that ka^2 + lb^2> c^2 for every sidelengths a,b,c

Source: Czech and Slovak Olympiad 2017, National Round, III A p2

February 2, 2020

inequalitiesgeometric inequality

Problem Statement

Find all pairs of real numbers

k, l

such that inequality

ka^2 + lb^2> c^2

applies to the lengths of sides

a, b, c

of any triangle.