Question 89
Prove that for any real numbers $x, y, z$ the following inequality is true:
$$
x^2(3y^2 + 3z^2 - 2yz) \geq yz(2xy + 2xz - yz).
$$
Find the triples that turn it into equality.
$$
x^2(3y^2 + 3z^2 - 2yz) \geq yz(2xy + 2xz - yz).
$$
Find the triples that turn it into equality.