All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
A simple inequality (Posted on 2014-12-31) Difficulty: 2 of 5
Given:
x>0, y>0, x+y=1

Prove that
(1 + 1/x)(1 + 1/y) ≥ 9.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: Solution Comment 4 of 4 |
(In reply to Solution by Bractals)

Another way

((x + 1)/x)((y+1)/y) >= 9

xy + x + y + 1 >= 9xy

But x + y = 1,

So we need 2 >= 8xy
or 1/4 >= xy

By symmetry, xy has its maximum when x = y = 1/2, 
so the maximum value of xy is 1/4.

q.e.d. 


  Posted by Steve Herman on 2014-12-31 15:58:47
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information