Nested in Inequailites

Algebra Level pending

Given that \( a+b+c+d+e=8\) and \(a^2+b^2+c^2+d^2+e^2=16 \). If the maximum value of \(e\) is in the form of \(\frac mn\) coprime positive integers \(m\) and \(n\), find the value of \(m+n\).

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