MathNet 2019-part-08 — 179 problems (EN–VI) Question 20

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 $a^{3}+b^{3}$.