1. Limited time only! Sign up for a free 30min personal 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!

How to satisfy this identity (conformal model in geometric algebra)

  1. Sep 9, 2011 #1

    I have the following equation in x and y: [tex]xy - \sqrt{(x^2+a^2)(y^2+c^2)} = -\frac{1}{a^2}-\frac{1}{c^2}[/tex] where the quantities a2 and c2 are given real constants, and I have to find real values for x, and y such that the equation above is always satisfied.

    Actually, I know that the solution should be: [itex]x = \frac{1-a^2}{2}[/itex], [itex]y = \frac{1-c^2}{2}[/itex], but I would like to know if there is a "mechanical" procedure to arrive at that solution, or if one has just to do "trial and error".

    PS: for anyone interested, solving this equation is useful for constructing the conformal model in Geometric Algebra.
    Last edited: Sep 9, 2011
  2. jcsd
  3. Sep 9, 2011 #2


    User Avatar
    Science Advisor

    Have you tried putting xy on the other side and then squaring both sides? The (xy)2 term will cancel.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: How to satisfy this identity (conformal model in geometric algebra)