Y by NYY, Adventure10, Mango247
Let
be two positive sequences defined by
and
for all
.
Prove that they are converges and find their limits.


![\[ \begin{cases} {{x}_{n+1}}{{y}_{n+1}}-{{x}_{n}}=0 \\ x_{n+1}^{2}+{{y}_{n}}=2 \end{cases} \]](http://latex.artofproblemsolving.com/2/0/1/2012dc6ff3a41478547cea4aa9b6bccbe17a3623.png)

Prove that they are converges and find their limits.
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