Question

Tìm GTNN của: A = x² - 2xy + 2y² + 2x - 10y + 33

Giúp e với ạ!!

Answer 1

\(A=x^2-2xy+2y^2+2x-10y+33\)

\(\Rightarrow A=\left(x^2+y^2+1-2xy+2x-2y\right)+\left(y^2-8y+16\right)+17\)

\(\Rightarrow A=\left(x-y+1\right)^2+\left(y-4\right)^2+17\ge17\)

Dấu "=" xảy ra khi và chỉ khi 

\(\left\{{}\begin{matrix}x-y+1=0\\y-4=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=4\end{matrix}\right.\)

Vậy \(GTNN\left(A\right)=17\left(tại.\left(x;y\right)=\left(3;4\right)\right)\)