1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Parametric representation

  1. Dec 11, 2006 #1
    Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational numbers for (aside from the trivial ones):


    Actually, I'm given the answer (which is really messy) and am supposed to show how to derive it. The book gives the hint to use a substitution x=X-Y, y=X+Y, u=U-V, and v=U+V and then factor the result in [itex]Q(\sqrt{-3})[/itex].

    The hint was easy to enact, but led to another dead end. I figure you can start by trying to find integer solutions, but that doesn't help either. In fact, I can't even figure out how to make any progress at all. Not even a little bit.

    Any clues out there at all?
  2. jcsd
  3. Dec 11, 2006 #2

    Gib Z

    User Avatar
    Homework Helper

    Are the capitals related in anyway to the lowercase counter parts or is that just a coincidence?
  4. Dec 12, 2006 #3
    I don't understand this question? The capitals are a change of variable, and I gave the formula for the new variables and how they relate to the old ones in the post?

    By the way, the new equation you get is:


    And factoring as the hint further suggests gives you:


    Which was the other dead end I hit. No idea what to do from there. In case it helps anyone get inspired, I'll write out the answer they give for x (small x), the others are similar. a,b and k are rational numbers:

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Parametric representation
  1. Base representation ~ (Replies: 1)