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I need to prove this inequality using AM-GM. Any help would be appreciated.

Let $a, b, c, d$ be non-negative numbers such that $a +b + c + d = 4$. Prove that: $$\frac4{abcd} \ge \frac ab + \frac bc + \frac cd + \frac da$$

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    Are you sure it is possible? Your inequality is cyclic, but not symmetric. If there are multiple stationary points (besides the one at $(1,1,1,1)$) the AM-GM inequality might be not powerful enough to prove the claim. Power mean inequalities tend to work only if there is a single stationary point. – 2017-01-02
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    http://math.stackexchange.com/questions/56395/prove-that-frac4abcd-geq-frac-a-b-frac-bc-frac-cd-frac-d-a?rq=1 – 2017-01-02
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    Note that the above link shows that this is a duplicate – 2017-01-02

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