1/ Ta có :

\(\left(2x+1\right)\left(y-5\right)=10\)

Vì \(x,y\in N\Leftrightarrow2x+1\in N,y-5\in N;2x+1,y-5\inƯ\left(10\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x+1=10\\y-5=1\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=1\\y-5=10\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=5\\y-5=2\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=2\\y-5=5\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{9}{2}\left(loại\right)\\y=6\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\y=15\end{matrix}\right.\\\left\{{}\begin{matrix}x=2\\y=7\end{matrix}\right.\\\left\{{}\begin{matrix}x=\dfrac{1}{2}\left(loại\right)\\y=10\end{matrix}\right.\end{matrix}\right.\)

Vậy --

2/ Gọi 3 số tự nhiên liên tiếp là \(a;a+1;a+2\left(a\in N\right)\)

\(\Leftrightarrow a+a+1+a+2\)

\(=3a+3⋮3\rightarrowđpcm\)