Finding limit

[Nobody1111]

Sequences a_n and b_n are defined in the follwing way:

a_1=x;
b_1=y;
where 0<x<y
and:
a_(n+1) = (a_n+b_n)/2
b_(n+1) = sqrt(a_(n+1)+b_n)

Proof, that both sequences are convergent to the same limit and find this limit.

Thanks a lot for any help.

[AKG]

You should be able to isolate and rearrange a bunch of times so that you get a_(n+1) and b_(n+1) in terms of a_n and b_n. See what you can do from there.