\(x=\frac{a+3}{3a}.\)
Để x có giá trị nguyên.
\(\Rightarrow\frac{a+3}{3a}\) có giá trị nguyên.
\(\Rightarrow a+3⋮3a\)
\(\Rightarrow3.\left(a+3\right)⋮3a\)
\(\Rightarrow3a+9⋮3a\)
Vì \(3a⋮3a.\)
\(\Rightarrow9⋮3a\)
\(\Rightarrow3a\inƯC\left(9\right)\)
\(\Rightarrow3a\in\left\{1;3;9;-1;-3;-9\right\}.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}3a=1\\3a=-1\end{matrix}\right.\\\left[{}\begin{matrix}3a=3\\3a=-3\end{matrix}\right.\\\left[{}\begin{matrix}3a=9\\3a=-9\end{matrix}\right.\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}a=\frac{1}{3}\\a=-\frac{1}{3}\end{matrix}\right.\left(KTM\right)\\\left[{}\begin{matrix}a=1\\a=-1\end{matrix}\right.\left(TM\right)\\\left[{}\begin{matrix}a=3\\a=-3\end{matrix}\right.\left(TM\right)\end{matrix}\right.\)
Vậy \(a\in\left\{1;-1;3;-3\right\}\) thì x là số nguyên.
Không chắc nha.
Chúc bạn học tốt!
