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- Feb 14, 2012

- 3,894

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Let $a,\,b,\,c$ and $d$ be four non-negative real numbers satisfying the condition

$2(ab+ac+ad+bc+bd+cd)+abc+abd+acd+bcd=16$

Prove that

$a+b+c+d\ge \dfrac{2}{3}(ab+ac+ad+bc+bd+cd)$

and determine when equality occurs.

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