Ta có:
\(2010x^2+2011y^2-4020x+4022y+4021=0\)
\(\Leftrightarrow(2010x^2-4020x+2010)+(2011y^2+4022y+2011)=0\)
\(\Leftrightarrow2010(x^2-2x+1)+2011(y^2+2y+1)=0\)
\(\Leftrightarrow2010(x-1)^2+2011(y+1)^2=0\)
Ta thấy:
\(\left\{{}\begin{matrix}2010\left(x-1\right)^2\ge0\forall x\\2011\left(y+1\right)^2\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow2010(x-1)^2+2011(y+1)^2\ge0\forall x,y\)
Mà \(\Leftrightarrow2010(x-1)^2+2011(y+1)^2=0\)
\(\Rightarrow\left\{{}\begin{matrix}2010\left(x-1\right)^2=0\\2011\left(y+1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)
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