D=\(-3x^2-5y^2+2x+7y-23\)
<=> D=\(-\left(3x^2+5y^2-2x-7y+23\right)\)
=\(-\left[3\left(x^2-2.\frac{2}{6}x+\frac{1}{9}\right)+5\left(y^2-2.\frac{7}{10}y+\frac{49}{100}\right)-\frac{1}{3}-\frac{49}{20}+23\right]\)
=\(-\left[3\left(x-\frac{1}{3}\right)^2+5\left(y-\frac{7}{10}\right)^2+\frac{1213}{60}\right]\)
Có \(3\left(x-\frac{1}{3}\right)^2+5\left(y-\frac{7}{10}\right)^2+\frac{1213}{60}\ge\frac{1213}{60}\)
<=> \(-\left[3\left(x-\frac{1}{2}\right)^2+5\left(y-\frac{7}{10}\right)^2+\frac{1213}{60}\right]\le-\frac{1213}{60}\) <=> \(D\le-\frac{1213}{60}\)
Dấu"=" xảy ra <=> \(\left\{{}\begin{matrix}x=\frac{1}{3}\\y=\frac{7}{10}\end{matrix}\right.\)
Vậy maxD=\(-\frac{1213}{60}\) <=> \(\left\{{}\begin{matrix}x=\frac{1}{3}\\y=\frac{7}{10}\end{matrix}\right.\)
