A difference in maxima and minima

Algebra Level 5

Given that the real numbers \(a\), \(b\), \(c\), \(d\), and \(e\) satisfy the equations:

\[a + b + c + d + e = 8\]

\[a^2 + b^2 + c^2 + d^2 + e^2 = 16,\]

the difference in the maximum and minimum values of \(a\) can be written as \(\frac {A}{B}\) where \(A\) and \(B\) are positive, coprime integers. Find the value of \(A + B\).


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