\(A=-3\left(x^2-\dfrac{2}{3}x\right)-5\left(y^2-\dfrac{7}{5}y\right)-23\\ A=-3\left(x^2-2\cdot\dfrac{1}{3}x+\dfrac{1}{9}\right)-5\left(y^2-2\cdot\dfrac{7}{10}y+\dfrac{49}{100}\right)+\dfrac{1}{3}+\dfrac{49}{20}-23\\ A=-3\left(x-\dfrac{1}{3}\right)^2-5\left(y-\dfrac{7}{10}\right)^2-\dfrac{1213}{60}\le-\dfrac{1213}{60}\\ A_{max}=-\dfrac{1213}{60}\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{3}\\y=\dfrac{7}{10}\end{matrix}\right.\)
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