MathDB
Inequality on the side lengths of a triangle - ILL 1990 YUG3

Source:

September 19, 2010
inequalitiesgeometryarea of a triangleinequalities unsolved

Problem Statement

Let a,b,ca, b, c be the side lengths and PP be area of a triangle, respectively. Prove that (a2+b2+c2−43P)(a2+b2+c2)≥2(a2(b−c)2+b2(c−a)2+c2(a−b)2).(a^2+b^2+c^2-4\sqrt 3 P) (a^2+b^2+c^2) \geq 2 \left(a^2(b - c)^2 + b^2(c - a)^2 + c^2(a - b)^2\right).
Back to ProblemsView on AoPS