# 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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