Question 61
Three positive real numbers $a$, $b$, $c$ with $a c = 9$ are given. It is known that for all real numbers $x$, $y$ with $x y \neq 0$ the following holds:
$$
\frac{a}{x^{2}} + \frac{b}{x y} + \frac{c}{y^{2}} \geq 0.
$$
What is the largest possible value of $b$?
(A) 1
(B) 3
(C) 6
(D) 9
(E) No such $b$ exists.
$$
\frac{a}{x^{2}} + \frac{b}{x y} + \frac{c}{y^{2}} \geq 0.
$$
What is the largest possible value of $b$?
(A) 1
(B) 3
(C) 6
(D) 9
(E) No such $b$ exists.