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2012 preRMO p12, 1/ \sqrt{2011+\sqrt{2011^2-1}}=\sqrt{m}-\sqrt{n}

Source:

June 16, 2019
algebra

Problem Statement

If 12011+20112−1=m−n\frac{1}{\sqrt{2011+\sqrt{2011^2-1}}}=\sqrt{m}-\sqrt{n}, where mm and nn are positive integers, what is the value of m+nm+n?
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