(2x+1).(y-5)=12. tìm các số tự nhiên x,y

Ta có: $2x+1$ và $y-5$ là $U\left(12\right)$

$12=1.12=2.6=3.4$

Vì $2x+1$ lẻ $\Rightarrow\left[{}\begin{matrix}2x+1=1\\2x+1=3\end{matrix}\right.$

$\left[{}\begin{matrix}2x+1=1\\2x+1=3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.$

$\left[{}\begin{matrix}y-5=12\\y-5=4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}y=17\\y=9\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=0;y=17\\x=1;y=9\end{matrix}\right.$

Vậy cặp $\left(x;y\right)$ thỏa mãn là: $\left(x=0;y=17\right);\left(x=1;y=9\right)$