Solving equation with two square roots



>>>>> "Poul" == Poul Riis  writes:

    Poul> To be more specific my question is:
    Poul> Is there a 'stronger' command than 'solve', or can I set some parameter so
    Poul> that maxima actually can solve an equation like
    Poul> solve(sqrt((x-a*e)^2+y^2)+sqrt((x+a*e)^2+y^2)=2*a,y);

I am not a very good maxima user, but here is a transcript of a
solution.  solve by itself doesn't produce a solution, but with some
more manipulations you can obtain a solution.  This assumes e above is
not %e.

(%i1) solve(sqrt((x-a*e)^2+y^2)+sqrt((x+a*e)^2+y^2)=2*a,y);
	     2	  2		 2  2		     2	  2		 2  2
(%o1) [sqrt(y  + x  + 2 a e x + a  e ) = 2 a - sqrt(y  + x  - 2 a e x + a  e )]
(%i2) part(%,1)^2;
       2    2		   2  2		       2    2		   2  2	 2
(%o2) y  + x  + 2 a e x + a  e  = (2 a - sqrt(y  + x  - 2 a e x + a  e ))
(%i3) solve(%,y);
Is  a - e x  positive, negative, or zero?

pos;
		   2  2	   2    2  2    2	      2	 2    2	   2  2	   2
(%o3) [y = - sqrt(e  x  - x  - a  e  + a ), y = sqrt(e  x  - x  - a  e  + a )]

Ray