olymmath

KöMaL 2011 A536

    The positive real numbers aa, bb, cc, dd satisfy aa+bb+cc+dd= abc + abd + acd + bcd . Prove that (a+b)(c+d)+(a+d)(b+c)≥4(1+ac)(1+bd).{(a+b)(c+d)}+(a+d)(b+c) \ge 4\sqrt{(1+ac)(1+bd)}.

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