August 19th, 2013, 06:17 AM  #1 
Newbie Joined: May 2013 Posts: 26 Thanks: 0  Inequality
Is this statement true for any x,y side of triangle 
August 19th, 2013, 08:17 AM  #2  
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Inequality Quote:
 
August 19th, 2013, 10:55 AM  #3 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Inequality
Actually the inequality is true for every positive x and y. Using arithmetic harmonic mean inequality we have 
August 21st, 2013, 04:17 AM  #4 
Newbie Joined: May 2013 Posts: 16 Thanks: 0  Re: Inequality
"Solution: 1/(2y+x)+1/(2x+y)=4/(x+y) if x, y side of triangle then this statement is not true." 
August 21st, 2013, 04:49 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,753 Thanks: 2136 
It's true if x = y and you have minus (instead of plus) signs in the denominators on the lefthand side. Nobody has suggested it works with the plus signs!

August 21st, 2013, 11:59 AM  #6 
Newbie Joined: May 2013 Posts: 26 Thanks: 0  Re: Inequality
So what is the final solution?!

August 21st, 2013, 12:21 PM  #7  
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: Inequality Quote:
 

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