Question 169
Find all nonnegative real numbers $a$, $b$, $c$ such that
$$
\frac{4a + 9b + 25c}{2a + 3b + 5c} + \frac{4b + 9c + 25a}{2b + 3c + 5a} + \frac{4c + 9a + 25b}{2c + 3a + 5b} = 10
$$
$$
\frac{4a + 9b + 25c}{2a + 3b + 5c} + \frac{4b + 9c + 25a}{2b + 3c + 5a} + \frac{4c + 9a + 25b}{2c + 3a + 5b} = 10
$$