Question 157
Suppose $a$, $b$, $c$ are real numbers, with $a + b + c = 3$. Prove that
$$
\frac{1}{5a^2 - 4a + 11} + \frac{1}{5b^2 - 4b + 11} + \frac{1}{5c^2 - 4c + 11} \le \frac{1}{4}.
$$
$$
\frac{1}{5a^2 - 4a + 11} + \frac{1}{5b^2 - 4b + 11} + \frac{1}{5c^2 - 4c + 11} \le \frac{1}{4}.
$$