Question 38
Prove that the real numbers $a$, $b$ fulfill
$$(x + y + z)^3 + a(x + y + z)(xy + xz + yz) + bxyz \ge 0,$$
for all $x, y, z \ge 0$, if and only if there exist $r \ge 0$, $s \ge 0$ such that $a = -4 + r$, $b = 9 - 9r + s$.
$$(x + y + z)^3 + a(x + y + z)(xy + xz + yz) + bxyz \ge 0,$$
for all $x, y, z \ge 0$, if and only if there exist $r \ge 0$, $s \ge 0$ such that $a = -4 + r$, $b = 9 - 9r + s$.