# Problem 303 Van Khea

If $a, b, x, y, z$ are positive real numbers such that $a+b=1$. Prove that
$\displaystyle x^3+y^3+z^3+6abxyz$$\geq (2a-b^2)(x^2y+y^2z+z^2x)+(2b-a^2)(xy^2+yz^2+zx^2)$