Let $a,b,c,d, e$ be real numbers such that they simultaneously satisfy the following equations $$a+b+c+d+e=8$$$$a^2+b^2+c^2+d^2+e^2=16$$Determine the smallest and largest value that $a$ can take.
Source: Mathematics Regional Olympiad of Mexico West 2018 P2
Tags: algebra, inequalities
Let $a,b,c,d, e$ be real numbers such that they simultaneously satisfy the following equations $$a+b+c+d+e=8$$$$a^2+b^2+c^2+d^2+e^2=16$$Determine the smallest and largest value that $a$ can take.