Question 74
Find all real numbers $a \gt 0$ such that there exist real numbers $x, y \gt 0$ with the properties
$$
x = a - \sqrt{y}, \quad y = a + \sqrt{x}, \quad \frac{x}{y} + \frac{y}{x} = 2023.
$$
$$
x = a - \sqrt{y}, \quad y = a + \sqrt{x}, \quad \frac{x}{y} + \frac{y}{x} = 2023.
$$