a/ \(\Leftrightarrow\left(a^2-4\right)x=a+2\)
Để pt có nghiệm duy nhất \(\Leftrightarrow a\ne\pm2\)
Khi đó \(x=\frac{a+2}{a^2-4}=\frac{1}{a-2}\)
Để x nguyên \(\Rightarrow a-2=Ư\left(1\right)=\left\{-1;1\right\}\)
\(\Rightarrow\left[{}\begin{matrix}a-2=-1\\a-2=1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a=1\\a=3\end{matrix}\right.\)
b/ \(\Leftrightarrow\left(a^2+a-2\right)x=3\left(a+2\right)\)
\(\Leftrightarrow\left(a-1\right)\left(a+2\right)x=3\left(a+2\right)\)
Để pt có nghiệm duy nhất \(\Leftrightarrow a\ne\left\{-2;1\right\}\)
Khi đó \(x=\frac{3\left(a+2\right)}{\left(a-1\right)\left(a+2\right)}=\frac{3}{a-1}\)
Để x nguyên \(\Rightarrow a-1=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)
\(a-1=-3\Rightarrow a=-2\) (loại)
\(a-1=-1\Rightarrow a=0\)
\(a-1=1\Rightarrow a=2\)
\(a-1=3\Rightarrow a=4\)
