Question 8
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 $m + n.$
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 $m + n.$