I have attached the original problem statement.
I'm not entirely sure how to show that the sequence is bounded. The book gave the hint of using the inequality ab<=1/2(a^2+b^2) to show xn+1>sqrt(a) for all n. I'm having trouble applying this inequality however, and am not really sure how to algebraically make use of it. I was looking at defining a and b for the variables, but what I am coming up with isn't making sense to me.
Part b I can do
Part c I was thinking of just working out algebraically by defining xn instead of xn-1 and changing the indexes. Does that sound like the right way to approach it.
I mostly would like some help with part a)