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