Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.3 National olympiad Prove it

78. Given that $a, b, c, d$ are positive numbers, prove: $(a+b)(b+c)(c+d)(d+a)(1+$ $\sqrt[4]{a b c d})^{4} \geqslant 16 a b c d(1+a)(1+b)(1+c)(1+d) .(2008$ Ukrainian Mathematical Olympiad)

Solution

None

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