Question

[Nguyễn Minh Giang]

Tìm GTNN của A
A= x² - 4xy + 5y² + 10x - 22y + 28 

Answer 1

[Nguyễn Việt Lâm]

\(A=\left(x^2-4xy+4y^2\right)+10\left(x-2y\right)+25+y^2-2y+1+2\) \(=\left(x-2y\right)^2+10\left(x-2y\right)+25+\left(y-1\right)^2+2\) \(=\left(x-2y+5\right)^2+\left(y-1\right)^2+2\)Do \(\left\{{}\begin{matrix}\left(x-2y+5\right)^2\ge0\\\left(y-1\right)^2\ge0\end{matrix}\right. \) ; \(\forall x;y\)\(\Rightarrow A\ge2\)\(A_{min}=2\) khi \(\left\{{}\begin{matrix}x-2y+5=0\\y-1=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-3\\y=1\end{matrix}\right.\)