Question 36
a) Infinitely many pairs of real numbers $(x, y)$ exist such that $x, y \in [0, \sqrt{3}]$ and the following equality holds: $x \cdot \sqrt{3-y^2} + y \cdot \sqrt{3-x^2} = 3$;
b) **No** pair of rational numbers $(x, y)$ exists such that $x, y \in [0, \sqrt{3}]$ and the following equality holds: $x \cdot \sqrt{3-y^2} + y \cdot \sqrt{3-x^2} = 3$.
b) **No** pair of rational numbers $(x, y)$ exists such that $x, y \in [0, \sqrt{3}]$ and the following equality holds: $x \cdot \sqrt{3-y^2} + y \cdot \sqrt{3-x^2} = 3$.