$\begin{cases} F^2+A^2+N^2 =3 \\ \min \left( F+A, A+N, F+N \right) > \sqrt 2 \\ \frac{F}{\left( A+N-F \right)^2}+\frac{A}{\left( N+F-A \right)^2}+\frac{N}{\left(F+A-N \right)^2} \geq \frac{S}{3000 \left( FAN \right)^2} \end{cases}$

For what maximum value of $S$ will the above conditions be always met simultaneously for positive real numbers $F,A$ and $N$ ?

**
Clarification:
**

- $FAN= F \times A \times N$ .

The answer is 9000.0.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

For Mcq lovers it's a great and interesting problem. Just assume f=a=n=1 as it would give the max. Value and also there's an interesting method to solve it