3. Vasya thought of two numbers. Their sum equals their product and equals their quotient. What numbers did Vasya think of?
Answer: $\frac{1}{2},-1$

Solution. Let the numbers be $x$ and $y$. Then, according to the problem, we have: $x+y=xy=\frac{x}{y}$.

From the equation $xy=\frac{x}{y}$, it follows that either $x=0$ and $y \neq 0$, or $y^{2}=1$, and $x$ can be any value. If $x=0$, from the equation $x+y=xy$ we get $y=0$, which is a contradiction. From the equation $y^{2}=1$, we obtain that either $y=1$ or $y=-1$. When $y=1$, there are no solutions to the equation $x+y=xy$, but when $y=-1$, from the equation $x+y=xy$ we get $x=\frac{1}{2}$.