(In reply to

Solution by FrankM)

"But c>=1, b>=2 and b-c>=1 so that (b-c)^2 + 2(b+c) - 7 >= 0"

-> But c>=1, b>=2 and b-c>=1 __with b+c >=3__ so that (b-c)^2 + 2(b+c) - 7 >= 0.

Very nice solution, which is concise and compact, yet precise. Also, the methodology inclusive of the said solution overrides the necessity to apply AM – GM inequality.

Consequently, I confirm having hyperlinked this methodology in my solution.

*Edited on ***May 20, 2008, 1:43 pm**