Ta có:\(n^2+10n+36=a^2\)
\(\Rightarrow n^2+10n+25+11=a^2\)
\(\Rightarrow\left(n+5\right)^2+11=a^2\)
\(\Rightarrow\left(n+5\right)^2-a^2=-11\)
\(\Rightarrow\left(n+5-a\right)\left(n+5+a\right)=-11\)
\(\Rightarrow\left(n+5-a\right)\left(n+5+a\right)=-1.11=1.-11\)
Ta có 2 TH sau
TH1:\(\hept{\begin{cases}n+5-a=-1\\n+5+a=11\end{cases}\Rightarrow2n+10=10\Rightarrow n=\frac{10-10}{2}=0}\)(nhận)
TH2:\(\hept{\begin{cases}n+5-a=1\\n+5+a=-11\end{cases}}\Rightarrow2n+10=-10\Rightarrow n=\frac{-10-10}{2}=-10\)(loại)
