You will be amazed with this

Algebra Level 5

{a+b+c+d+e=8a2+b2+c2+d2+e2=16\begin{cases} a&+&b&+&c&+&d&+&e&=&8 \\ a^2&+&b^2&+&c^2&+&d^2&+&e^2&=&16 \\ \end{cases}

Given that the real numbers a,b,c,d,ea, b, c, d, e satisfy the system of equations above, find the sum of the maximum and minimum possible value of aa.

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