MathCastle
Proof WritingHardDirect Proof

Direct Proof · Hard problem

To prove a2+b2+c2≥ab+bc+caa^2 + b^2 + c^2 \ge ab + bc + ca, one writes 2(a2+b2+c2−ab−bc−ca)=(a−b)2+(b−c)2+(c−a)22(a^2 + b^2 + c^2 - ab - bc - ca) = (a - b)^2 + (b - c)^2 + (c - a)^2. Exactly when does equality hold?