Question 63
Let $x$ and $y$ be two non-negative real numbers. Show that
$$
\left(x^{2}+x+1\right)\left(y^{2}+y+1\right) \geqslant 9 x y .
$$
What are the cases of equality?
$$
\left(x^{2}+x+1\right)\left(y^{2}+y+1\right) \geqslant 9 x y .
$$
What are the cases of equality?