Rid polynomial of square-root



Russell Shaw wrote:
> Hi,
> Starting with:
>
>   x = sqrt(x^2 + 1) - a
>
> How do i get it into the form:
>
>   x^2(b^2 - 1) + 2*a*b*x + a^2 - 1 = 0
>
>
> Also, i tried to solve for x:
>
>                     2
> (%o1)     x = sqrt(x  + 1) + a
>
> (%i2) solve(%, x);
>
>
> It just gives:
>                     2
> (%o2)    [x = sqrt(x  + 1) + a]
>
> I've read all the manuals.
>
You can solve it "by hand" using maxima.  Where does where b come into it?

(%i1) x=sqrt(x^2+1)-a;
                                       2
(%o1)                        x = sqrt(x  + 1) - a
(%i2) %+a;
                                           2
(%o2)                        x + a = sqrt(x  + 1)
(%i3) lhs(%)^2=rhs(%)^2;
                                      2    2
(%o3)                          (x + a)  = x  + 1
(%i4) expand(%);
                            2            2    2
(%o4)                      x  + 2 a x + a  = x  + 1
(%i5) lhs(%)-rhs(%)=0;
                                       2
(%o5)                         2 a x + a  - 1 = 0
(%i6) solve(%,x);
                                        2
                                       a  - 1
(%o6)                           [x = - ------]
                                        2 a