Question 58
Show that for all positive real numbers $x$, $y$ and $z$
$$
\frac{x^2+1}{(x+y)^2+4(z+1)} + \frac{y^2+1}{(y+z)^2+4(x+1)} + \frac{z^2+1}{(z+x)^2+4(y+1)} \ge \frac{1}{2}
$$
$$
\frac{x^2+1}{(x+y)^2+4(z+1)} + \frac{y^2+1}{(y+z)^2+4(x+1)} + \frac{z^2+1}{(z+x)^2+4(y+1)} \ge \frac{1}{2}
$$