[Maxima] one question about Maxima

[Richard Fateman]

There are many things that solve will not do automatically because they 
are heuristics which may or may not introduce extraneous roots, and/or 
because they may be expensive. Or they just weren't programmed (yet).

  This does not prevent you from trying them yourself before calling 
solve, of course.

If you want to poke at the solve program, there are also issues like 
this one.

(-sqrt(2)*sqrt(25*sqrt(2)*sqrt(5)-3)-6*sqrt(5)*sqrt(sqrt(2)*sqrt(5)+3)+13*sqrt(2)*sqrt(sqrt(2)*sqrt(5)+3))*x=4

solve(%,x);

Solve gives you one solution, but there are no solutions, because the 
equation is equivalent to  0*x=4.

(Try proving that :)

RJF
  (who originally wrote the solve program in about 1969)