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!

Difficult inequality

  1. Jun 14, 2008 #1
    Pls help me to prove the following inequality:

    3 (a/b + b/a + b/c + c/b + a/c + c/a) + (1 + a) (1 + b) (1 + c) (c/b + c/a) (b/a + b/c) (a/b + a/c)

    >=

    6 abc + 6 + 9(ab + bc + ac + a + b + c) + 3((ab)/c + (bc)/a + (ac)/b)

    with a, b, c are positive reals

    If it helps, I know the equality occurs when a=b=c=2 (although I'm not sure if it's the only one).

    Also, can any one helps to prove (2, 2, 2) is the only point at which equality occurs.

    Thanks a lot...

    Any hint is appreciated...
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...