\begin{equation*} \begin{cases} 2x + 3y = 2a^2 - 12a + 8 | * 3 &\\ 3x - 2y = 3a^2 + 8a + 12 | * -2 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 6x + 9y = 6a^2 - 36a + 24 &\\ -6x + 4y = -6a^2 - 16a - 24 & \end{cases} \end{equation*}
$6x + 9y - 6x + 4y = 6a^2 - 36a + 24 - 6a^2 - 16a - 24$
13y = −52a
y = −52a : 13
y = −4a;
\begin{equation*} \begin{cases} 2x + 3y = 2a^2 - 12a + 8 | * 2 &\\ 3x - 2y = 3a^2 + 8a + 12 | * 3 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 4x + 6y = 4a^2 - 24a + 16 &\\ 9x - 6y = 9a^2 + 24a + 36 & \end{cases} \end{equation*}
$4x + 6y + 9x - 6y = 4a^2 - 24a + 16 + 9a^2 + 24a + 36$
$13x = 13a^2 + 52$
$x = \frac{13a^2 + 52}{13}$
$x = a^2 + 4$.
$x + y = a^2 + 4 - 4a = a^2 - 4a + 4 = (a - 2)^2 ⩾ 0$
Наименьшим значение буде при:
$(a - 2)^2 = 0$
a − 2 = 0
a = 2