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TOT 199 1988 Autumn S2 a^2pq+b^2qr+c^2rp <= 0 for sidelengths, p+q+r=0

Source:

March 7, 2021

geometric inequalityinequalities

Problem Statement

Prove that

a^2pq + b^2qr + c^2rp \le 0

, whenever

a, b

and

c

are the lengths of the sides of a triangle and

p + q + r = 0

.
( J. Mustafaev , year 12 student, Baku)