Question 75
Suppose $a$, $b$, and $c$ are positive real numbers. Prove that,
$$
24abc \leq |a^3 + b^3 + c^3 - (a+b+c)^3| \leq \frac{8}{9}(a+b+c)^3,
$$
and that for both inequalities, equality occurs if and only if $a = b = c$.
$$
24abc \leq |a^3 + b^3 + c^3 - (a+b+c)^3| \leq \frac{8}{9}(a+b+c)^3,
$$
and that for both inequalities, equality occurs if and only if $a = b = c$.