\(A=x^2+5y^2+5x-16y+32\)
\(\Leftrightarrow A=x^2+5y^2+5x-16y+\dfrac{25}{4}+\dfrac{64}{5}+\dfrac{259}{20}\)
\(\Leftrightarrow A=\left(x^2+5x+\dfrac{25}{4}\right)+\left(5y^2-16y+\dfrac{64}{5}\right)+\dfrac{259}{20}\)
\(\Leftrightarrow A=\left[x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2\right]+5\left(y^2-\dfrac{16}{5}y+\dfrac{64}{25}\right)+\dfrac{259}{20}\)
\(\Leftrightarrow A=\left(x+\dfrac{5}{2}\right)^2+5\left[y^2-2.y.\dfrac{8}{5}+\left(\dfrac{8}{5}\right)^2\right]+\dfrac{259}{20}\)
\(\Leftrightarrow A=\left(x+\dfrac{5}{2}\right)^2+5\left(y-\dfrac{8}{5}\right)^2+\dfrac{259}{20}\)
Vậy GTNN của \(A=\dfrac{259}{20}\) khi \(\left\{{}\begin{matrix}x+\dfrac{5}{2}=0\Rightarrow x=\dfrac{-5}{2}\\y-\dfrac{8}{5}=0\Rightarrow y=\dfrac{8}{5}\end{matrix}\right.\)
