11: \(A=x^2-2x+y^2+4y+8\)
\(=x^2-2x+1+y^2+4y+4+3\)
\(=\left(x-1\right)^2+\left(y+2\right)^2+3>=3\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-1=0\\y+2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)
13: \(3x^2-4xy+2y^2-3x+2007\)
\(=2x^2-4xy+2y^2+x^2-3x+\dfrac{9}{4}+2007-2,25\)
\(=2\left(x-y\right)^2+\left(x-\dfrac{3}{2}\right)^2+2004,75>=2004,75\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}x-y=0\\x-\dfrac{3}{2}=0\end{matrix}\right.\Leftrightarrow x=y=\dfrac{3}{2}\)
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