\(\left\{{}\begin{matrix}x^2+2x+1=y^2+11\\\left(x+1\right)^2-y^2=11\\\Rightarrow\left(x+1\right)^2=36\Rightarrow\left[{}\begin{matrix}x=5\\x=-7\end{matrix}\right.\end{matrix}\right.\) \(\)
Vậy: \(\left(x,y\right)=\left(5,5\right);\left(5,-5\right);\left(-7,5\right);,\left(-7,-5\right)\)