Tìm GTNN: A = x^2 - 2xy + 2y^2 + 2x - 10y +17
Tìm GTNN: A = x2 − 2xy + 2y2 + 2x − 10y +17.
A = x2 − 2xy + 2y2 + 2x − 10y +17
= (x2 − 2xy + y2) + 2(x − y) + 1 + (y2 − 8y +16)
= (x − y)2 + 2(x − y) + 1 + (y − 4)2
= (x − y + 1)2 + (y − 4)2 ≥ 0.
Vậy GTNN của A bằng 0 khi \(\left\{ \begin{array}{l}x - y + 1 = 0\\y - 4 = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = 3\\y = 4\end{array} \right.\).