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MMO 310 Moscow MO 1955 given 6-variable inequality, triangle sides exist?

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August 17, 2019
inequalitiessidelengths of triangleTriangle

Problem Statement

Let the inequality Aa(Bb+Cc)+Bb(Aa+Cc)+Cc(Aa+Bb)>ABc2+BCa2+CAb22Aa(Bb + Cc) + Bb(Aa + Cc) + Cc(Aa + Bb) > \frac{ABc^2 + BCa^2 + CAb^2}{2} with given a>0,b>0,c>0a > 0, b > 0, c > 0 hold for all A>0,B>0,C>0A > 0, B > 0, C > 0. Is it possible to construct a triangle with sides of lengths a,b,ca, b, c?
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