Question 6
Depending on the positive integer $k$, determine the smallest real number $D_k$ such that
$$
(abc)^2 + (bcd)^2 + (cda)^2 + (dab)^2 \le D_k
$$
for all nonnegative real numbers $a, b, c, d$ such that $a^k + b^k + c^k + d^k = 4$.
$$
(abc)^2 + (bcd)^2 + (cda)^2 + (dab)^2 \le D_k
$$
for all nonnegative real numbers $a, b, c, d$ such that $a^k + b^k + c^k + d^k = 4$.