HMMT 2019 A3

Let $x$ and $y$ be positive real numbers. Define $a=1+\frac{x}{y}$ and $b=1+\frac{y}{x}$ . If $a^{2}+b^{2}=15$ , compute $a^{3}+b^{3}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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