Question 69
Consider four positive real numbers $a$, $b$, $c$ and $d$, satisfying
$$
a^2 + ab + b^2 = 3c^2 \quad \text{and} \quad a^3 + a^2b + ab^2 + b^3 = 4d^3.
$$
Prove that
$$
a + b + d \le 3c.
$$
$$
a^2 + ab + b^2 = 3c^2 \quad \text{and} \quad a^3 + a^2b + ab^2 + b^3 = 4d^3.
$$
Prove that
$$
a + b + d \le 3c.
$$