We have:

a1 = 2, a(n+1) = (an^2 +2) / 2an

Then comes the induction proof:

" Use mathematical induction to show that: an>= 0 for all n"

This should also mean that a(n+1) is greater than, or equal to 0. So that:

a(n+1) >= 0

(an^2 +2) / 2an >= 0

an^2 +2 >= 0

Where do I go from here?

Or could I just say that an has to be greater than 0, because if an=0 then the denominator for a(n+1) would be 0?