verify that the iteration x_{i+1}=x_{i}^{2}-2 will converge to solution epsilon=2 of the equation x^2-x-2=0 only of for some n0 all iterates xn with n>=n0 are equal to 2 ie only accidently

in this do i have to prove or just verify

if i have to prove then how?

i know

x(n+1)=g(x(n))

interval [a,b]

a<=x<=b , a<=g(x)<=b and mod of first derivative of g is less than 1