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

Home > Just Math
Sum and Ratio Sum (Posted on 2011-01-16) Difficulty: 3 of 5
Determine all possible quadruplets (A, B, P, Q) of positive integers, with P ≤ Q, that satisfy this system of equations:

A + B = 21, and:

A/P2 + B/Q2 = 1

Prove that these are the only quadruplets that exist.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Possible solution | Comment 2 of 4 |

Simply recasting the equation as:

(a*(q-p)(q+p))/(q^2-21)=p^2


gives solutions {a,p,q} at {5,3,6}{12,4,6}{37,6,24}{41,6,12}{48,6,9}{85,9,36}{101,9,18}...etc. of which only the first two have a less than 21, compliant with the stipulations of the problem.


  Posted by broll on 2011-01-17 02:08:11
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 (9)
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