Prove AM-GM Inequality: a,b,c ≥ 0 and a+b+c=3

[klajv]

Can't figure this out and hope to get some help, TIA!

a,b,c >= 0 and a+b+c=3
Prove that a²+b²+c²+ab+bc+ca >= 6

 

[disregardthat]

Write the left hand side of the inequality differently, using the expression for (a+b+c)^2.

You will arrive upon the inequality ab+bc+ac <= 3 = a+b+c. Now, can you prove ab+bc+ac <= (a+b+c)(a+b+c)/3 ?

 

[klajv]

disregardthat <---

Yes, thanks a lot