8. Find $\sqrt{\frac{x}{63}-32} \times \sqrt{\frac{y}{63}-32}$, given that $\frac{1}{x}+\frac{1}{y}=\frac{1}{2016}$.

ANSWER: 32.
Solution: Let's make the substitution: $a=x / 63, b=y / 63$. Then we can rewrite the condition as: find $\sqrt{(a-32) \cdot(b-32)}$, given that $\frac{1}{a}+\frac{1}{b}=\frac{1}{32}$, i.e., $a b=32(a+b)$. Transforming: $\sqrt{(a-32) \cdot(b-32)}=\sqrt{a b-32(a+b)+1024}=32$.