Nested in Inequailites

Algebra Level pending

Given that $$a+b+c+d+e=8$$ and $$a^2+b^2+c^2+d^2+e^2=16$$. If the maximum value of $$e$$ is in the form of $$\frac mn$$ coprime positive integers $$m$$ and $$n$$, find the value of $$m+n$$.

×