# [Maxima] problem solving radical equations

Barton Willis willisb at unk.edu
Mon Jan 29 08:35:36 CST 2007

```maxima-bounces at math.utexas.edu wrote on 01/29/2007 05:07:22 AM:

> Trying to solve a system of equations with radicals, i get an error
message:
>
> (%i1) solve([x+3*y=5,sqrt(x+y)-1=y]);
>
> `algsys' cannot solve - system too complicated.
>  -- an error.  Quitting.  To debug this try debugmode(true);

(%i2) e : [x+3*y=5,sqrt(x+y)-1=y]\$
(%i3) ep : map('topoly,e);
(%o3) [3*y+x-5=0,y^2+y-x+1=0]
(%i4) sol : algsys(ep,[x,y]);
(%o4) [[x=11-6*sqrt(2),y=2*sqrt(2)-2],[x=6*sqrt(2)+11,y=-2*sqrt(2)-2]]
(%i5) for si in sol do print(float(subst(si,e)));
[5.0=5.0,0.82842712474619=0.82842712474619]
[5.000000000000002=5.0,2.82842712474619=-4.82842712474619]

The function topoly potentially makes the solution set larger. It seems
that sol[1] is a solution, but sol[2] isn't.  The float method for
checking solutions is crude, but I think that a symbolic check
would involve denesting square roots.  Maybe you can get
Maxima to check the solutions symbolically.

Barton
```