On Mon, Jan 2, 2012 at 12:14 AM, <leon.magiera at wp.pl> wrote:
> Hi
>
> Problem 1
> How, using Maxima, to solve in elegant way the equation
>
> eq:sqrt(x+3-4*sqrt(x-1))+sqrt(x+8-6*sqrt(x-1))=1;
>
> The solution is
>
> 5<=x<=10
>
It looks like to_poly_solver can solve this:
(%i54) load(to_poly_solver);
(%o54) "/Users/rtoy/src/sourceforge/maxima/share/contrib/to_poly_solver.mac"
(%i55) to_poly_solve(eq,x);
(%o55) %union(%if(?%and(-%pi/2 < parg(3-%c41),-%pi/2 < parg(%c41-2),
-%pi/2 < parg(%c41),parg(3-%c41) <= %pi/2,
parg(%c41-2) <= %pi/2,parg(%c41) <= %pi/2),
[x = %c41^2+1],%union()))
This is kind of hard to read, but basically if the complex number %c41
satisfies the conditions in the %if, then %c41^2+1 is a solution. If we're
interested in just real solutions, I think the %if simplifies to 2<= %c41
<= 3, which means 5 <= x <= 10.
Ray