# Difficult inequality

1. Jun 14, 2008

### LanNguyen

Pls help me to prove the following inequality:

3 (a/b + b/a + b/c + c/b + a/c + c/a) + (1 + a) (1 + b) (1 + c) (c/b + c/a) (b/a + b/c) (a/b + a/c)

>=

6 abc + 6 + 9(ab + bc + ac + a + b + c) + 3((ab)/c + (bc)/a + (ac)/b)

with a, b, c are positive reals

If it helps, I know the equality occurs when a=b=c=2 (although I'm not sure if it's the only one).

Also, can any one helps to prove (2, 2, 2) is the only point at which equality occurs.

Thanks a lot...

Any hint is appreciated...