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Am-gm inequality?

  1. Aug 4, 2011 #1
    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. jcsd
  3. Aug 4, 2011 #2

    disregardthat

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    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 ?
     
  4. Aug 4, 2011 #3
    disregardthat <---

    Yes, thanks alot
     
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