Question 14
a) Find $x \in \mathbb{N}$ and $y \in \mathbb{Q}$, such that $\sqrt{x + \sqrt{x}} = y$.
b) Prove that one can find infinitely many pairs $(x, y) \in \mathbb{Q}^2$ such that
$$
\sqrt{x + \sqrt{x}} = y.
$$
b) Prove that one can find infinitely many pairs $(x, y) \in \mathbb{Q}^2$ such that
$$
\sqrt{x + \sqrt{x}} = y.
$$