Question 84
Find the maximum value of
$$
\frac{1}{a^2 - 4a + 9} + \frac{1}{b^2 - 4b + 9} + \frac{1}{c^2 - 4c + 9}
$$
where $a$, $b$, $c$ are non-negative real numbers satisfying $a + b + c = 1$.
$$
\frac{1}{a^2 - 4a + 9} + \frac{1}{b^2 - 4b + 9} + \frac{1}{c^2 - 4c + 9}
$$
where $a$, $b$, $c$ are non-negative real numbers satisfying $a + b + c = 1$.