Question 36
Prove that if $x, y, z$ are non-negative numbers, then
$$
x^3 + y^3 + z^3 + 3xyz \geq x^2(y + z) + y^2(z + x) + z^2(x + y).
$$
Determine the cases of equality.
$$
x^3 + y^3 + z^3 + 3xyz \geq x^2(y + z) + y^2(z + x) + z^2(x + y).
$$
Determine the cases of equality.