\(Q=\left|x-2010\right|+\left(y+2011\right)^{2010}+2011\)
Ta có:\(\hept{\begin{cases}\left|x-2010\right|\ge0\\\left(y+2011\right)^{2010}\ge0\end{cases}}\)
Nên \(\left|x-2010\right|+\left(y+2011\right)^{2010}+2011\ge2011\)
Vậy \(Q_{min}=2011\Leftrightarrow\hept{\begin{cases}x-2010=0\\y+2011=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2010\\y=-2011\end{cases}}\)