kill(all)$

van=facebook.com/LearningCalculus$

X(r):=r-2/r*sqrt(r^2-1)$
Y(r):=2/r$
x(r):= sqrt(X(r)^2+Y(r)^2)$ x(r);

f(r):= sqrt(2*r^2-4*sqrt(r^2-1))-3;

newton(t):=float(subst(t,r,r-f(r)/diff(f(r),r)))$
R:newton(newton(3.27759678531684));

x(R);