(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: \(\left(x=0;y=17\right);\left(x=1;y=9\right)\)