kill(all)$

van=facebook.com/LearningCalculus$

f(x):=x-3$

g(x):=sqrt(x)+1/sqrt(x)$

h(x):=''(f(x)-g(x));

newton(t):=float(subst(t,x,x-h(x)/diff(h(x),x)));

x0 : newton(newton(newton(newton(newton(5.82842712474619)))));

X0:(3+2*sqrt(2));

h(X0);

fpprec:40$

bfloat(fullratsimp(h((3+2*sqrt(2)))));

fpprec:79$

bfloat(fullratsimp(h((3+2*sqrt(2)))));

fullratsimp(sqrt(X0)-1/sqrt(X0));

f(x)-g(x);

h(x);

k(x):=sqrt(x)-1/sqrt(x);

h(x)-k(x);

h(X0)-k(X0);

bfloat(%);