Question 170
If the nonnegative real numbers $x$, $y$ and $z$ have sum $2$, prove that
$$
x^2y^2 + y^2z^2 + z^2x^2 + xyz \le 1.
$$
For which values of $x$, $y$ and $z$ is equality valid?
$$
x^2y^2 + y^2z^2 + z^2x^2 + xyz \le 1.
$$
For which values of $x$, $y$ and $z$ is equality valid?