Question 178
Find all real numbers $k$, such that the inequality
$$
a^3 + b^3 + c^3 + d^3 + 1 \ge k(a+b+c+d)
$$
holds for any $a, b, c, d \in [-1, +\infty)$.
$$
a^3 + b^3 + c^3 + d^3 + 1 \ge k(a+b+c+d)
$$
holds for any $a, b, c, d \in [-1, +\infty)$.