perplexus.info :: Just Math : Sum and Ratio Sum

Sum and Ratio Sum (Posted on 2011-01-16)

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.)

First Tiny Start (Spoiler)

| Comment 1 of 4

Well, obviously, P can only be 2, 3, 4.

If P = 1, then A/P²is >= 1

And A/P² + B/Q²<=A/P² + B/P²= 21/P²

So, if P >= 5, then A/P² + B/Q² <= 21/25

Edited on January 16, 2011, 1:32 pm

Posted by Steve Herman on 2011-01-16 13:27:58

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 (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info