Question 170
Let $x$, $y$, $z$ be real numbers from segment $[0; 1]$. Prove that
$$
(x^4 + y^4 + z^4) + (x^5 + y^5 + z^5) + (x - y)^6 + (y - z)^6 + (z - x)^6 \le 6.
$$
$$
(x^4 + y^4 + z^4) + (x^5 + y^5 + z^5) + (x - y)^6 + (y - z)^6 + (z - x)^6 \le 6.
$$