\(A=x^2-2xy+2y^2-4y+5\)
\(A=\left(x^2-2xy+y^2\right)+\left(y^2-4y+4\right)+1\)
\(A=\left(x-y\right)^2+\left(y-2\right)^2+1\)
Vì \(\left(x-y\right)^2\ge0\) với mọi x,y
\(\left(y-2\right)^2\ge0\) với mọi y
\(\Rightarrow\left(x-y\right)^2+\left(y-2\right)^2\ge0\) với mọi x,y
\(\Rightarrow\left(x-y\right)^2+\left(y-2\right)^2+1\ge1\)
\(\Rightarrow Amin=1\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\y-2=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=y\Rightarrow x=2\\y=2\end{matrix}\right.\)
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