Question

Tìm GTNN của :

\(5x^2+y^2-4xy-2y+2030\)

Answer 1

\(A=5\left(x^2-2x.\dfrac{2}{5}y+\dfrac{4}{25}y^2\right)+\dfrac{1}{5}\left(y^2-10y+25\right)+2025\)

\(A=5\left(x-\dfrac{2y}{5}\right)^2+\dfrac{1}{5}\left(y-5\right)^2+2025\ge2025\)

\(\Rightarrow A_{min}=2025\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}y-5=0\\x-\dfrac{2y}{5}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=5\\x=2\end{matrix}\right.\)