kill(all)$

van=facebook.com/LearningCalculus$

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

f(x):=2*x^3 - 3*x -sqrt(1-x^2)*(1-6*x^2);

a : -1/sqrt(2*(5 + 2*sqrt(5)))$
newton(a)$ bfloat(a)$

b: 1/sqrt(2)$
newton(b)$ bfloat(b)$

c: sqrt((1/10)*(5 + 2*sqrt(5)))$
newton(c)$ bfloat(c)$

[a,b,c];