From: ivgroups@onlinehome.de   
      
   "Richard Fateman" wrote in   
   news:331553de-1632-f445-d391-d8be6d6a8bc7@cs.berkeley.edu...   
   > How can I solve a bit more complex radical equations in Maple or   
   > Mathematica?   
   > An example:   
   > p0 + p1*y + p2*y^2 - x = (y - sqrt(a0 + a1*x + a2*x^2)) * (y - sqrt(b0 +   
   > b1*x + b2*x^2))   
   > solve(%,{a0,a1,a2,b0,b1,b2}) seems to be not the right way.   
   > I need a procedure that collects the equations for the coefficients of   
   > each power of x and solves this radical equations automatically.   
   > usually you isolate one of the sqrts and square both sides.   
   > isolate the other sqrt, and square both sides.   
   > then you have a polynomial equation of substantial degree in x,y,p1,p2..   
   > which you can either solve or not.   
   This commonly known method works only for simple radical equations. It does   
   not work for a sum of a greater number of root terms on one side of the   
   equation. I examined when this method does work and when not.   
   The general method for more complicated radical equations is to substitute   
   each different radical-containing summand by a new variable name and to   
   solve the resulting equation system.   
   The method that you proposed is to solve such equations manually. But it   
   would be nice if there would exist a software command or algorithm for this   
   task.   
   My problem is to check simply if a term contains a radical or not.   
      
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