\(A=y^2-2y\left(x-1\right)+\left(x-1\right)^2-\left(x-1\right)^2+2x^2+4x+5\)
\(A=\left(y-x+1\right)^2-x^2+2x-1+2x^2+4x+5\)
\(A=\left(y-x+1\right)^2+x^2+6x+9-5\)
\(A=\left(y-x+1\right)^2+\left(x+3\right)^2-5\ge-5\)
Vậy Amin là -5 \(\Leftrightarrow\left\{{}\begin{matrix}\left(y-x+1\right)^2=0\\\left(x+3\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=-4\end{matrix}\right.\)
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ta có : A=2x2 + y2-2xy +4x+2y+5
= (x2+y2+2y+1-2x-2xy)+(x2+6x
+9)-5
= (x-y-1)2+(x+3)2-5>=-5
Vậy Min A=-5 \(\Leftrightarrow\)x=-3; y=-4
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