Question 99
Show that
$$
\frac{1}{x + y^{20} + z^{11}} + \frac{1}{y + z^{20} + x^{11}} + \frac{1}{z + x^{20} + y^{11}} \le 1
$$
for all positive real numbers $x, y, z$ satisfying $xyz = 1$.
$$
\frac{1}{x + y^{20} + z^{11}} + \frac{1}{y + z^{20} + x^{11}} + \frac{1}{z + x^{20} + y^{11}} \le 1
$$
for all positive real numbers $x, y, z$ satisfying $xyz = 1$.