# Complicated Inequality

**Algebra**Level 5

Find the maximum value of \(N\) which satisfies the following inequality over all positive reals \(a,b\) and \(c\):

\[\sqrt{abc}(\sqrt{a}+\sqrt{b}+\sqrt{c})+(a+b+c)^2\geq N\sqrt{3abc(a+b+c)}.\]

Find the maximum value of \(N\) which satisfies the following inequality over all positive reals \(a,b\) and \(c\):

\[\sqrt{abc}(\sqrt{a}+\sqrt{b}+\sqrt{c})+(a+b+c)^2\geq N\sqrt{3abc(a+b+c)}.\]

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