Đáp án:
\(\left[ \begin{array}{l}
x = 21\\
x = - 11\\
x = 13\\
x = - 3\\
x = 7\\
x = 3\\
x = 9\\
x = 1\\
x = 6\\
x = 4
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \dfrac{{{x^2} - 3x + 6}}{{x - 5}}\\
= \dfrac{{{x^2} - 10x + 25 + 7x - 19}}{{x - 5}}\\
= \dfrac{{{{\left( {x - 5} \right)}^2} + 7\left( {x - 5} \right) + 16}}{{x - 5}}\\
= \left( {x - 5} \right) + 7 + \dfrac{{16}}{{x - 5}}\\
A \in Z\\
\Leftrightarrow \dfrac{{16}}{{x - 5}} \in Z\\
\Leftrightarrow \left[ \begin{array}{l}
x - 5 = 16\\
x - 5 = - 16\\
x - 5 = 8\\
x - 5 = - 8\\
x - 5 = 2\\
x - 5 = - 2\\
x - 5 = 4\\
x - 5 = - 4\\
x - 5 = 1\\
x - 5 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 21\\
x = - 11\\
x = 13\\
x = - 3\\
x = 7\\
x = 3\\
x = 9\\
x = 1\\
x = 6\\
x = 4
\end{array} \right.
\end{array}\)
