Question 48
Prove that
$$
(x^2 + y^2 z^2) \cdot (y^2 + x^2 z^2) \cdot (z^2 + x^2 y^2) \geq 8 x y^2 z^3
$$
holds for all integer values of $x$, $y$ and $z$. When does equality hold?
$$
(x^2 + y^2 z^2) \cdot (y^2 + x^2 z^2) \cdot (z^2 + x^2 y^2) \geq 8 x y^2 z^3
$$
holds for all integer values of $x$, $y$ and $z$. When does equality hold?