Đặt n + 24 = a2
n - 65 = b2
=> a2 - b2 = n + 24 - n + 65
=> (a - b)(a + b) = 1 . 89
Vì a - b < a + b
\(\Rightarrow\hept{\begin{cases}a-b=1\\a+b=89\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}a=45\\b=44\end{cases}}\)
=> n + 24 = 452
=> n = 2001
Đặt \(n+24=a^2\)
\(n-65=b^2\)
\(\Rightarrow a^2-b^2=\left(n+24\right)-\left(n-65\right)\)
\(\Rightarrow a^2-b^2=n+24-n+65\)
\(\Rightarrow\left(a-b\right)\left(a+b\right)=1.89\)
Vì \(a-b< a+b\)
\(\Rightarrow\hept{\begin{cases}a-b=1\\a+b=89\end{cases}}\)\(\Rightarrow\hept{\begin{cases}a=45\\b=44\end{cases}}\)
\(\Rightarrow n+24=45^2\)
\(\Rightarrow n=2001\)
