Question 57
Let $x$, $y$, $z$ be real numbers satisfying $y \gt 2z \gt 4x$ and
$$
2(x^3 + y^3 + z^3) + 15(xy^2 + yz^2 + zx^2) \gt 16(x^2y + y^2z + z^2x) + 2xyz.
$$
Show that $4x + y \gt 4z$.
$$
2(x^3 + y^3 + z^3) + 15(xy^2 + yz^2 + zx^2) \gt 16(x^2y + y^2z + z^2x) + 2xyz.
$$
Show that $4x + y \gt 4z$.