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

  1. Sep 9, 2011 #1
    Hello,

    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

    mathman

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    Science Advisor
    Gold Member

    Have you tried putting xy on the other side and then squaring both sides? The (xy)2 term will cancel.
     
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