Russell Shaw a ?crit :
> 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
There is no b in your starting equation.
Maybe the equation is
b*x = sqrt(x^2 + 1) - a ;
>
>
> 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.
>
This may go in the direction you want :
(%i2) eq:x = sqrt(x^2 + 1) - a ;
(%o2) x = sqrt(x^2+1)-a
(%i3) solve(eq^2,x);
Is a positive or negative?
p;
(%o3) [x = -(a^2-1)/(2*a),x = (a^2-1)/(2*a)]
(%i4) solve(eq,x^2);
Is x+a positive, negative, or zero?
p;
(%o4) [x^2 = x^2+2*a*x+a^2-1]
In case you start with b*x = sqrt(x^2 + 1) - a my second method
gives your expected expression, the first one doesn't work.
Eric