\begin{equation*} \begin{cases} x - 5y = a^2 + 10a + 1 | * -4 &\\ 4x + y = 4a^2 - 2a + 4 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} -4x + 20y = -4a^2 - 40a - 4 &\\ 4x + y = 4a^2 - 2a + 4 & \end{cases} \end{equation*}
$-4x + 20y + 4x + y = -4a^2 - 40a - 4 + 4a^2 - 2a + 4$
21y = −42a
y = −42a : 21
y = −2a;
\begin{equation*} \begin{cases} x - 5y = a^2 + 10a + 1 &\\ 4x + y = 4a^2 - 2a + 4 | * 5 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} x - 5y = a^2 + 10a + 1 &\\ 20x + 5y = 20a^2 - 10a + 20 & \end{cases} \end{equation*}
$x - 5y + 20x + 5y = a^2 + 10a + 1 + 20a^2 - 10a + 20$
$21x = 21a^2 + 21$
$x = \frac{21(a^2 + 1)}{21}$
$x = a^2 + 1$
$x - y = a^2 + 1 + 2a = a^2 + 2a + 1 = (a + 1)^2 ⩾ 0$
Наименьшим значение буде при:
$(a + 1)^2 = 0$
a + 1 = 0
a = −1