# Recurring Styles #3 - A Twisted Recurrence!

Algebra Level 5

$\large{x_{n+2} = \dfrac{x_nx_{n+1}}{5x_n - 4x_{n+1}}}$

with $$x_0 = 2; x_1 = 3$$.

Let $$(x_n)_{n=0}^\infty$$ be a sequence that satisfies the above recurrence relation. Then find the value of $$\large{{\left\lfloor \frac{x_{10}}{x_{20}} \right\rfloor}}$$.

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