Question 37
Prove that for positive real numbers $x, y, z$,
$$
\frac{xyz(x + y + z + \sqrt{x^2 + y^2 + z^2})}{(x^2 + y^2 + z^2)(xy + yz + zx)} \le \frac{3 + \sqrt{3}}{9}.
$$
$$
\frac{xyz(x + y + z + \sqrt{x^2 + y^2 + z^2})}{(x^2 + y^2 + z^2)(xy + yz + zx)} \le \frac{3 + \sqrt{3}}{9}.
$$