Inequality: $2(p^2+q^2+r^2)+2(pq+qr+rp)\ge pqr$ I need to determine the range of $p,q,r$ such that $2(p^2+q^2+r^2)+2(pq+qr+rp)\ge pqr$. I am not given any other information except that $p,q,r\in \mathbb{R}$. I haven't solved a problem like this before, so I'm really stuck. I'm thinking that it might be true for all real numbers $p,q,r$ but then I would need a proof but I couldn't find one.
Thanks!
EDIT: Sorry, I forgot to add:
I wrote it as $(p+q)^2+(q+r)^2+(r+p)^2\ge pqr$.

This doesn't hold true in general.
For example, let $p=q=r$, you will get $$12p^2\geq p^3.$$ You can see it is not true when $p>12$.
