Question 97
Let $x$, $y$ and $z$ be nonnegative real numbers. Knowing that
$$
2(xy + yz + zx) = x^2 + y^2 + z^2,
$$
prove
$$
\frac{x + y + z}{3} \geq \sqrt[3]{2xyz}.
$$
$$
2(xy + yz + zx) = x^2 + y^2 + z^2,
$$
prove
$$
\frac{x + y + z}{3} \geq \sqrt[3]{2xyz}.
$$