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

Home > Just Math
Just prove it (Posted on 2013-10-20) Difficulty: 2 of 5
Prove that:
If (x+sqrt{1+y^2})*(y+sqrt{1+x^2})=1,
then
x+y=0 .

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Doing it backwards | Comment 1 of 4
Well, it is easy enough to prove that if 
x+y=0
then
(x+sqrt{1+y^2})*(y+sqrt{1+x^2})=1 

Just substitute y = -x in the messy formula, and do the multiplication, and simplify.

Unfortunately, that doesn't prove that this is the only solution.

Squaring both sides of the equation didn't seem to help.

I guess that some more clever substitution is called for, but I'm not finding it.  I tried c = x + y, with a hope of proving that c = 0, but substituting y = c-x didn't seem to help either.

This problem is a difficulty 2?  I will be very interested to see the solution.


  Posted by Steve Herman on 2013-10-21 09:19:44
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 (1)
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