5. Find all real numbers $x$ and $y$ that satisfy the equation

$$
(x+y)^{2}=(x+3)(y-3)
$$

Solve the problem independently. You have 150 minutes for solving.

The use of notes, literature, or a pocket calculator is not allowed.

Mathematical Competition for High School Students in Slovenia

## Invitational Competition

March 28, 2003

## Problems for 4th Year