Question 64
Let $a$, $b$ and $c$ be positive real numbers such that $a \gt b + c$. Prove that
$$
(a^2 - b^2 - c^2)(a^5 - b^5 - c^5) \le (a^3 - b^3 - c^3)(a^4 - b^4 - c^4).
$$
$$
(a^2 - b^2 - c^2)(a^5 - b^5 - c^5) \le (a^3 - b^3 - c^3)(a^4 - b^4 - c^4).
$$