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!

Prove an inequality

  1. Apr 18, 2015 #1
    Is it possible to prove this:
    x^x + y^y < (x+y)^(x+y) for every x,y >=1 ?
     
  2. jcsd
  3. Apr 18, 2015 #2

    RaulTheUCSCSlug

    User Avatar
    Gold Member

    Well, let me think, since I am not really sure if this would work for all parameters of x and y.... never mind, you have x,y >1! What you could do is take the derivative of both equations to measure it's change in slope, and if (x+y)^(x+y)is greater, then it will have a change in slope that is greater then the other equation. But I am not sure if that is what you want.
     
  4. Apr 18, 2015 #3
    Iam just proving it,just expand the Right side (x+y)^(x+y), u get x multiplied by x+y times which is obviously greater than x^x and same in case of y and remaining terms of expansion are positive as x,y>1 and no negative terms in expansion. hope it helps.
     
  5. Apr 18, 2015 #4
    Thanks for the answers, but I would prefer an algebraic solution.
    I did what Raul said with the graph but I would like an algebraic sol.
    I believe that it is solved algebraically and it is not a transcendental equation.
     
    Last edited: Apr 18, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove an inequality
  1. Proving Inequalities (Replies: 1)

  2. Prove inequality (Replies: 19)

Loading...