Let the lengths of the sides of triangle ABC be denoted by a,b, and c, using the standard notations. Let G denote the centroid of triangle ABC. Prove that for an arbitrary point P in the plane of the triangle the following inequality is true: a⋅PA3+b⋅PB3+c⋅PC3≥3abc⋅PG.Proposed by János Schultz, Szeged inequalitiesgeometrykomal