Question

[Nguyễn Mạnh Việt Bách]

tìm min của D=\(^{x^2-2xy+6y^2-12x+2y+45}\)

Answer 1

[Nguyễn Việt Lâm]

\(D=\left(x^2-2xy+y^2\right)-12\left(x-y\right)+36+5y^2+9\)

\(=\left(x-y\right)^2-12\left(x-y\right)+36+5y^2+9\)

\(=\left(x-y-6\right)^2+5y^2+9\)

Do \(\left\{{}\begin{matrix}\left(x-y-6\right)^2\ge0\\5y^2\ge0\end{matrix}\right.\) ;\(\forall x;y\)

\(\Rightarrow D\ge9\)

\(D_{min}=9\) khi \(\left\{{}\begin{matrix}x-y-6=0\\5y^2=0\end{matrix}\right.\) \(\Rightarrow\left(x;y\right)=\left(6;0\right)\)