# Five five five and five!

Algebra Level 4

Let $$a, b, c, d, e \in R^{+}$$, their sum is equal to 8 and their sum of squares is equal to 16. If the maximum value of $$e$$ can be written as $$\frac{A}{B}$$, when $$A$$ and $$B$$ are coprime positive integers. Find $$A + B$$.

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