Đáp án:
\(\left[ \begin{array}{l}
x = 5\\
x = - 7\\
x = 2\\
x = - 4\\
x = 1\\
x = - 3\\
x = 0\\
x = - 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
{x^2} + 5 \vdots x + 1\\
\to {x^2} + 2x + 1 - 2x + 4 \vdots x + 1\\
\to {\left( {x + 1} \right)^2} - 2x + 4 \vdots x + 1\\
\to - 2x + 4 \vdots x + 1\\
\to - 2\left( {x + 1} \right) + 6 \vdots x + 1\\
\to 6 \vdots x + 1\\
\to x + 1 \in U\left( 6 \right)\\
\to \left[ \begin{array}{l}
x + 1 = 6\\
x + 1 = - 6\\
x + 1 = 3\\
x + 1 = - 3\\
x + 1 = 2\\
x + 1 = - 2\\
x + 1 = 1\\
x + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 5\\
x = - 7\\
x = 2\\
x = - 4\\
x = 1\\
x = - 3\\
x = 0\\
x = - 2
\end{array} \right.
\end{array}\)
