4. There are two distinct real numbers which are larger than their reciprocals by 2 . Find the product of these numbers.
Answer: -1
Solution: Let $x$ be one of these real numbers. We have $x=\frac{1}{x}+2$, which is equivalent to $x^{2}-2 x-1=0$. The required real numbers are the two distinct roots of this quadratic equation, which have a product of -1 .