kill(all)$

fpprec:100;

fpprintprec:30;

van=facebook.com/LearningCalculus$

      Newton's Method using 100 digit precision arithmetic

f(x):= 48*x^(1/4) + 12/sqrt(x) + 84 -
       1/x^(3/4) + 47/x^(1/4) + 96*sqrt(x);

newton(t):=bfloat(subst(t,x,x-f(x)/diff(f(x),x)));

a:newton(newton( 1.77018777444687185323237199839b-5));

b:bfloat(1/(4+2*4^(1/3))^4);

is(equal(a,b));