Help with Sequences (Recurrence Relations)

Put both in terms of a
a= U(n+1) / (Un +10) and a = sqrt ( V(n+1) / (Vn +16)
Can you see where to go from here?

Sorry I have no idea, this question is miles from anything we've done before.

I presume you know how to solve a basic recurrence relation.

For the first one, call the limit u, and rearrange your resulting equation to get u= "some function of a"

Similarly for the second one to get v= "another function of a"

You're told that v=u, so equate the two and solve for a.

We have $U_{n+1} = aU_n + 10$.
Let L be the common limit. Then $U_n \to L$ and so $U_{n+1} \to L$ also.
So we must have $L = aL + 10$.

A similar argument holds for V. This gives two equations linking L and a. Solve them to find L and a.