Để cho gọn thì đặt \(\left\{{}\begin{matrix}2010-a=x\\2012-b=y\end{matrix}\right.\)
\(VT=\left|x\right|+\left|1+x\right|+\left|3+x\right|+\left|y\right|\)
\(VT=\left|-x\right|+\left|3+x\right|+\left|1+x\right|+\left|y\right|\)
\(VT\ge\left|-x+3+x\right|+\left|1+x\right|+\left|y\right|\)
\(VT\ge3+\left|1+x\right|+\left|y\right|\ge3\)
Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}1+x=0\\y=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=2011\\b=2012\end{matrix}\right.\)
\(a^2-b^2=-4023\)
