Product of Years

Algebra Level 5

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

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

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

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

Find a+b+cd+ea+b+c-d +e.

This problem is not original.


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