Question 51
Suppose $a$, $b$, $c$, $d$ are positive numbers such that
$$
1 = 3abcd + 2(abc + bcd + dca + dab) + (ab + bc + cd + da + ac + bd).
$$
Prove that
$$
abcd \le \frac{1}{81},
$$
and that the inequality is strict unless $a = b = c = d = 1/3$.
$$
1 = 3abcd + 2(abc + bcd + dca + dab) + (ab + bc + cd + da + ac + bd).
$$
Prove that
$$
abcd \le \frac{1}{81},
$$
and that the inequality is strict unless $a = b = c = d = 1/3$.