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a,b,c are sidelengths if 5abc>a^3+b^3+c^3

Source: Czech and Slovak Match 2000 P1

December 5, 2022
geometryGeometric Inequalitiesinequalitiesalgebra

Problem Statement

a,b,ca,b,c are positive real numbers which satisfy 5abc>a3+b3+c35abc>a^3+b^3+c^3. Prove that a,b,ca,b,c can form a triangle.
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