Question 24
Given real numbers $x, y, z$ such that $x + y + z = 0$, show that
$$
\frac{x(x+2)}{2x^2+1} + \frac{y(y+2)}{2y^2+1} + \frac{z(z+2)}{2z^2+1} \ge 0.
$$
When does equality hold?
$$
\frac{x(x+2)}{2x^2+1} + \frac{y(y+2)}{2y^2+1} + \frac{z(z+2)}{2z^2+1} \ge 0.
$$
When does equality hold?