kill(all)$

van=facebook.com/LearningCalculus$

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):=(4+r^2+(-1+r^2)^(1/2)*(-4))^(1/2);

x(R);