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I have the following equation inxandy: [tex]xy - \sqrt{(x^2+a^2)(y^2+c^2)} = -\frac{1}{a^2}-\frac{1}{c^2}[/tex] where the quantitiesaand^{2}care given real constants, and I have to find real values for^{2}x, andysuch 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.

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

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