Question 157
Prove that for all positive real numbers $x, y, z$,
$$
x^3(y^2 + z^2)^2 + y^3(z^2 + x^2)^2 + z^3(x^2 + y^2)^2 \ge xyz[xy(x+y)^2 + yz(y+z)^2 + zx(z+x)^2].
$$
$$
x^3(y^2 + z^2)^2 + y^3(z^2 + x^2)^2 + z^3(x^2 + y^2)^2 \ge xyz[xy(x+y)^2 + yz(y+z)^2 + zx(z+x)^2].
$$