2005 AIME II Problems/Problem 8

Problem

The equation $2^{333x-2}+2^{111x+2}=2^{222x+1}+1$ has three real roots. Given that their sum is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, find $m+n$ .

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2005 AIME II Problems/Problem 8

Problem

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