# Am-gm inequality?

1. Aug 4, 2011

### 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

2. Aug 4, 2011

### 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 ?

3. Aug 4, 2011

### klajv

disregardthat <---

Yes, thanks alot
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