a) Ta có :
\(a+2\inƯ\left(7\right)=\left\{1;7;-1;-7\right\}\)
\(\Rightarrow a\in\left\{-1;5;-3;-9\right\}\)
Vậy \(a\in\left\{-1;5;-3;-9\right\}\) là giá trị cần tìm
b) Ta có :
\(2a+5⋮a-2\)
Mà \(a-2⋮a-2\)
\(\Rightarrow\left\{{}\begin{matrix}2a+5⋮a-2\\2a-4⋮a-2\end{matrix}\right.\)
\(\Rightarrow9⋮a-2\)
Vì \(a\in Z\Rightarrow a-2\in Z;a-2\inƯ\left(9\right)\)
Ta có bảng :
| \(a-2\) | \(1\) | \(3\) | \(9\) | \(-1\) | \(-3\) | \(-9\) |
| \(a\) | \(3\) | \(5\) | \(11\) | \(1\) | \(-1\) | \(-7\) |
| \(Đk\)\(a\in Z\) | TM | TM | TM | TM | TM | TM |
Vậy \(a\in\left\{3;5;11;1;-1;-7\right\}\) là giá trị cần tìm
\(a+2\inƯ\left(7\right)\)
\(Ư\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(x\in\left\{-1;-3;5;-9\right\}\)
\(2a+5⋮a-2\)
\(2a-4+9⋮a-2\)
\(2\left(a-2\right)+9⋮a-2\)
\(\Leftrightarrow9⋮a-2\)
\(\Rightarrow a-2\inƯ\left(9\right)\)
\(Ư\left(9\right)=\left\{\pm1;\pm3;\pm9\right\}\)
\(a=\left\{3;1;5;-1;11;-7\right\}\)
hihi
