TR-MO 2005 Problem 1

Tüm $a, b, c, d$ pozitif gerçel sayıları için,

$\sqrt{a^4+c^4}+\sqrt{a^4+d^4}+\sqrt{b^4+c^4}+\sqrt{b^4+d^4} \geq 2\sqrt{2}\,(ad+bc)$

olduğunu gösteriniz.

Official text Turkish Mathematical Olympiad 2005 official paper, page 1. Quoted with source.

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