Ta thấy :
\(\left\{{}\begin{matrix}\left(a-2009\right)^2\ge0\\\left(b+2010\right)^2\ge0\end{matrix}\right.\)
Mà \(\left(a-2009\right)^2+\left(b+2010\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(a-2009\right)^2=0\\\left(b+2010\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a-2009=0\\b+2010=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=2009\\b=-2010\end{matrix}\right.\)
Vậy ............
\(\left(a-2009\right)^2+\left(b+2010\right)^2=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left(a-2009\right)^2=0\\(b+2010)^2=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a-2009=0\\b+2010=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a=2009\\b=-2010\end{matrix}\right.\)
vậy \(a=2009\)
\(b=-2010\)
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