# Arbab Qamar

Algebra Level 5

$\begin{cases} a^2+b^2+c^2+d^2+e^2 = 25 \\ a+2b+c+ d \sqrt{3}+e = 13\end{cases}$

If $$a,b,c,d$$ and $$e$$ are real numbers satisfying the two equation above, find the sum of the minimum and maximum possible values of $$e$$.

If you got your answer as $$\dfrac{A}{B}$$, where $$A$$ and $$B$$ are coprime positive integers, submit your answer as $$A\times B$$.

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