Mock AIME 6 2006-2007 Problems/Problem 8

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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Mock AIME 6 2006-2007 Problems/Problem 8

Problem

Solution