Not an Irriational III

Algebra Level 5

\[\begin{cases} X=-3-4\left(2-\sqrt{1-5\left(2-\sqrt{1-6\left(2-\sqrt{1-7(2-...)}\right)}\right)}\right) \\ Y=\dfrac 1{4-7\left(4-\sqrt{4-9\left(4-\sqrt{4-11(4-...)}\right)}\right)} \end{cases} \]

Find \(\dfrac{1}{XY}\).

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