Question 20
Find the smallest positive number $m$ such that there exists unique function $f: \mathbb{R}^+ \to \mathbb{R}^+$ such that
$$
f(x + f(y)) = f(x) + \frac{mx^5 f(y)}{f(x)^2} + f(y^2), \forall x, y \gt 0.
$$
$$
f(x + f(y)) = f(x) + \frac{mx^5 f(y)}{f(x)^2} + f(y^2), \forall x, y \gt 0.
$$