# Product of Years

Algebra Level 5

$\large (x + 2010)(x + 2011)(x + 2012)(x + 2013) = 5$

If the maximum real value of $$x$$ such that the above equation is true can be expressed in simplest terms as

$\large \frac{\sqrt{a+ b\sqrt{c}} -d}{e}$

For positive integers $$a,b,c,d,e$$ with $$c$$ square-free, and $$\gcd (a,e) = 1$$.

Find $$a+b+c-d +e$$.

This problem is not original.

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