This question has come to my attention: Prove this inequality with $xyz\le 1$. It has been locked and it seems appropriate to make a meta post about it. I'm not requesting to unlock, I just think there should be a meta post about it.
Note that the OP has asked the same question here and indeed it seems to be an Australian TST problem (if that's relevant).
The reason why the question is locked is not clear to me.