Question 75
Find all functions $f : \mathbb{R} \to [0, \infty)$ such that, for all real $a, b, c, d$ that satisfy $ab + bc + cd = 0$, the following equality holds:
$$
f(a - b) + f(c - d) = f(a) + f(b + c) + f(d)
$$
(Here $\mathbb{R}$ is the set of real numbers and $[0, \infty)$ is the set of nonnegative real numbers.)
$$
f(a - b) + f(c - d) = f(a) + f(b + c) + f(d)
$$
(Here $\mathbb{R}$ is the set of real numbers and $[0, \infty)$ is the set of nonnegative real numbers.)