Question 33
Let $\mathbb{R}$ denote the set of all real numbers. Find all pairs of functions $f: \mathbb{R} \to \mathbb{R}$ and $h: \mathbb{R}^2 \to \mathbb{R}$ such that
$$
f(x + y - z)^2 = f(xy) + h(x + y + z, xy + yz + zx)
$$
for all $x, y, z \in \mathbb{R}$.
$$
f(x + y - z)^2 = f(xy) + h(x + y + z, xy + yz + zx)
$$
for all $x, y, z \in \mathbb{R}$.