No, the answer is not 2.500

Algebra Level 5

\[ \begin{eqnarray} &&\sqrt{ \dfrac a{b+c+d+e}} + \sqrt{ \dfrac b{a+c+d+e}} + \sqrt{ \dfrac c{a+b+d+e}} \\ && + \sqrt{ \dfrac d{a+b+c+e}} + \sqrt{ \dfrac e{a+b+c+d}} \end{eqnarray}\]

Over all non-negative real numbers \(a,b,c,d\) and \(e\), find the infimium value of the expression above.

Give your answer to 3 decimal places.

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