Question 102
The real numbers $x$, $y$, $z$ and $A$ satisfy the relation
$$
A = \sqrt{\frac{1}{(2x - y - z)^2} + \frac{1}{(2y - z - x)^2} + \frac{1}{(2z - x - y)^2}}
$$
Show that if $x$, $y$ and $z$ are rational numbers, then $A$ is also a rational number.
$$
A = \sqrt{\frac{1}{(2x - y - z)^2} + \frac{1}{(2y - z - x)^2} + \frac{1}{(2z - x - y)^2}}
$$
Show that if $x$, $y$ and $z$ are rational numbers, then $A$ is also a rational number.