Answer

`a,` $\text{Vì}$ `x , y \in NN` $\text{nên}$ `2x - 1 , y + 2 \in NN`

`=> 2x - 1 , y + 2 \in Ư(32) = {1 ; 2 ; 4 ; 8 ; 16 ; 32}`

$\text{Lập bảng giá trị:}$

$\begin{array}{|c|c|c|}\hline 2x - 1&1&2&4&8&16&32\\\hline y + 2&32&16&8&4&2&1\\\hline x&1&\dfrac{3}{2}&\dfrac{5}{2}&\dfrac{9}{2}&\dfrac{17}{2}&\dfrac{33}{2}\\\hline y&30&14&6&2&0&-1\\\hline \text{Thử lại}&\text{TM}&\text{KTM}&\text{KTM}&\text{KTM}&\text{KTM}&\text{KTM}\\\hline\end{array}$

$\text{Vậy}$ `(x , y) = (1 , 30)`

__________________________

`b,` $\text{Ta có:}$ `x + 17 \vdots x + 2`

$\text{Mà:}$ `x + 2 \vdots x + 2`

$\text{Lập hiệu:}$ 

`(x + 17) - (x + 2)`

`= x + 17 - x - 2`

`= (x - x) + (17 - 2)`

`= 15 \vdots x + 2`

$\text{Vì}$ `x \in NN` $\text{nên}$ `x + 2 \in NN`

`=> x + 2 \in Ư(15) = {1 ; 3 ; 5 ; 15}`

$\text{Lập bảng giá trị:}$

$\begin{array}{|c|c|c|}\hline x + 2&1&3&5&15\\\hline x&-1&1&3&13\\\hline \text{Thử lại}&\text{KTM}&\text{TM}&\text{TM}&\text{TM}\\\hline\end{array}$

$\text{Vậy}$ `x \in {1 ; 3 ; 13}`