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

Home > Numbers
Classical Rules 1 (Posted on 2006-04-17) Difficulty: 3 of 5
Find three positive rational numbers such that their sum is a square, and the sum of any pair exceeds the third by a square.

Classical Rules: Let a "square" be any number that is the square of a rational number.

No Solution Yet Submitted by goFish    
Rating: 3.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Full solution | Comment 4 of 10 |
Let the numbers be a, b, and c. We have a+b+c=t, a+b=c+z, a+c=b+y, and b+c=a+x. Summing the last three, we find x+y+z=t, and then a=(y+z,), b=(x+z), and c=(x+y).

A way to find appropriate x, y, z, and t, is picking x and y randomly, and then factoring so x+y= t-z= (t+z)(t-z).

An example: I picked x=4 and y=7; then, (t+z)(t-z)=63, so I can choose t=8 and z=1, finally leading to a=25, b=17/2, and c=65/2.

  Posted by Federico Kereki on 2006-04-17 14:59:53
Please log in:
Remember me:
Sign up! | Forgot password

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

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information