Question 81
Prove that
$$
\sqrt{a^4 + c^4} + \sqrt{a^4 + d^4} + \sqrt{b^4 + c^4} + \sqrt{b^4 + d^4} \ge 2\sqrt{2}(ad + bc)
$$
for all real numbers $a$, $b$, $c$, $d$.
$$
\sqrt{a^4 + c^4} + \sqrt{a^4 + d^4} + \sqrt{b^4 + c^4} + \sqrt{b^4 + d^4} \ge 2\sqrt{2}(ad + bc)
$$
for all real numbers $a$, $b$, $c$, $d$.