Найдите наименьшее значение A=2x^2+y^2-6x-2xy.

\[A = 2x^{2} + y^{2} - 6x - 2xy =\]

\[= \left( x^{2} - 2xy + y^{2} \right) + \left( x^{2} - 6x + 9 \right) - 9 =\]

\[= (x - y)^{2} + (x - 3)^{2} - 9\]

\[x - 3 = 0\]

\[x = 3.\]

\[y = x = 3.\]

\[Наименьшее\ значение\ \]

\[\ A = - 9\ при\ x = 3;y = 3.\]