1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Am-gm inequality?
  1. An inequality (Replies: 11)

  2. AM:GM inequality (Replies: 1)

  3. Inequality Proof (Replies: 3)

Loading...