Question

Aratati ca :a patrat+b patrat+c patrat>ab+bc+ca(mai mare sau egal)

Answer 1

$(a-b)^{2} \geq 0 \\ a^{2} + b^{2} \geq 2ab \\ b^{2}+ c^{2} \geq 2bc \\ c^{2} + a^{2} \geq 2ac \\ Adunam\ relatiile \ si\ impartim\ la\ 2 .\Obtinem \\ a^{2} + b^{2}+ c^{2} \geq ab+bc+ac$