The undocumented function to_poly_solve can solve this equation.
To use to_poly_solve, you'll need to load the file "topoly_solver."
An example:
(%i4) load("topoly_solver")$
(%i5) to_poly_solve(abs(x)=2,x);
(%o5) [[x=2],[x=-2]]
If you want to find all complex solutions, to_poly_solve doesn't work:
(%i6) declare(x,complex)$
(%i7) to_poly_solve(abs(x)=2,x);
(%o7) [[x=2],[x=-2]]
The to_poly_solver tries to solve algebraic equations, but it cannot solve
trigonometric, exponential, or logarithmic equations.
To_poly_solver is in /share/contrib (not in the /src) for several reasons:
it isn't as well tested as other parts of Maxima; it has no user
documentation;
and the way to_poly_solve works might change (in particular, the
representation
of solutions).
If you have questions or comments about to_poly_solve, let us know.
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>????????1.?I?want?to?solve?(abs(x)=2),but?the?ans?as?follow:
>(%i9)?abs(x)=2;
>(%o9)?????????????????????????????abs(x)?=?2
>(%i10)?solve(%);
>(%o10)???????????????????????????[abs(x)?=?2]
>?there?is?no?solve?!