Results 1 to 3 of 3

Thread: need help to prove inequalities

  1. September 2nd 2011, 03:07 AM #1
    Mhmh96
    Mhmh96 is offline
    Member
    Joined
    Sep 2011
    Posts
    149

    need help to prove inequalities

    Hello..

    I need help to prove this inequalities
    Follow Math Help Forum on Facebook and Google+
  2. September 4th 2011, 12:50 PM #2
    Aryth
    Aryth is offline
    Super Member Aryth's Avatar
    Joined
    Feb 2007
    From
    USA
    Posts
    615
    Thanks
    1
    Awards
    1
    MHF Donor

    Re: need help to prove inequalities

    I don't know how good you are at inequalities but it basically goes like this:

    \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} = \frac{a^2cd}{abcd} + \frac{b^2ad}{abcd} + \frac{c^2ab}{abcd} + \frac{d^2bc}{abcd}


    = \frac{a^2cd + b^2ad + c^2ab + d^2bc}{abcd} \leq \frac{a^2 + b^2 + c^2 + d^2}{abcd} \leq \frac{a + b + c + d}{abcd} \leq \frac{4}{abcd}

    So, \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} \leq \frac{4}{abcd}
    Follow Math Help Forum on Facebook and Google+
  3. September 4th 2011, 12:55 PM #3
    alexmahone
    alexmahone is offline
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,071
    Thanks
    6

    Re: need help to prove inequalities

    Quote Originally Posted by Aryth View Post
    = \frac{a^2cd + b^2ad + c^2ab + d^2bc}{abcd} \leq \frac{a^2 + b^2 + c^2 + d^2}{abcd} \leq \frac{a + b + c + d}{abcd}
    Care to explain the first inequality?

    The second inequality is false. Take a = 3, b = 0.3, c = 0.3, d = 0.4 for a counterexample.
    Last edited by alexmahone; September 4th 2011 at 01:07 PM.
    Follow Math Help Forum on Facebook and Google+
« proof x/(-y) = (-x)/y | Worded Question »

Similar Math Help Forum Discussions

  1. Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 24th 2010, 05:55 AM
  2. Mathematical Induction to Prove Inequalities
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: November 28th 2009, 07:09 PM
  3. Using triangle inequality to prove inequalities
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 24th 2008, 10:50 AM
  4. HELP with INEQUALITIES
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 7th 2008, 02:36 PM
  5. some inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: March 25th 2007, 01:47 PM

Search Tags


/mathhelpforum @mathhelpforum