Question 15
Find all positive real numbers $x$, $y$, $z$ if
$$
\frac{1}{x^2+1} + \frac{1}{y^2+4} + \frac{1}{z^2+9} = \frac{7}{12} \sqrt{\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}}.
$$
$$
\frac{1}{x^2+1} + \frac{1}{y^2+4} + \frac{1}{z^2+9} = \frac{7}{12} \sqrt{\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}}.
$$