1. [3] Positive real numbers $x, y$ satisfy the equations $x^{2}+y^{2}=1$ and $x^{4}+y^{4}=\frac{17}{18}$. Find $x y$.
Answer: $\frac{1}{6}$ We have $2 x^{2} y^{2}=\left(x^{2}+y^{2}\right)^{2}-\left(x^{4}+y^{4}\right)=\frac{1}{18}$, so $x y=\frac{1}{6}$.