Mock AIME 6 2006-2007 Problems/Problem 8

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Problem

A sequence of positive reals defined by $a_0=x$, $a_1=y$, and $a_n\cdot a_{n+2}=a_{n+1}$ for all integers $n\ge 0$. Given that $a_{2007}+a_{2008}=3$ and $a_{2007}\cdot a_{2008}=\frac 13$, find $x^3+y^3$.

Solution

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