Question 43
Let $a, b, c$ be any real numbers such that $a + b + c = 0$. Prove that
$$
\frac{33a^2 - a}{33a^2 + 1} + \frac{33b^2 - b}{33b^2 + 1} + \frac{33c^2 - c}{33c^2 + 1} \ge 0.
$$
$$
\frac{33a^2 - a}{33a^2 + 1} + \frac{33b^2 - b}{33b^2 + 1} + \frac{33c^2 - c}{33c^2 + 1} \ge 0.
$$