# Maximum Value of Eh?

Algebra Level 4

$\begin{eqnarray} a^{2}+b^{2}+c^{2}&=&2014 \\ a+2b+3c&=&86 \end{eqnarray}$

Let $$a,b,c$$ be real numbers such that they satisfy the system of equations above.

The maximum value of $$a$$ can be expressed as $$\dfrac{m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers. Find the value of $$m+n$$.

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