y = \(\dfrac{\left(x-8\right)^2-48}{x+5}\)
<=> y = \(\dfrac{x^2-16x+16}{x+5}\)
<=> y = \(\dfrac{x\left(x+5\right)-21\left(x+5\right)+121}{x+5}\)
<=> y = x - 21 + \(\dfrac{121}{x+5}\)
y đạt giá trị nguyên <=> 121 chia hết cho (x + 5) <=> (x + 5) là ước của 121 <=> x + 5 ∈ \(\left\{1;-1;11;-11;121;-121\right\}\)
<=> x + 5 = 1 <=> \(\left\{{}\begin{matrix}x=-4\\y=96\end{matrix}\right.\left(loai\right)\)
x + 5 = -1 <=> \(\left\{{}\begin{matrix}x=-6\\y=-148\end{matrix}\right.\) (loai)
x + 5 = 11 <=> \(\left\{{}\begin{matrix}x=6\\y=-4\end{matrix}\right.\) (loai)
x + 5 = -11 <=> \(\left\{{}\begin{matrix}x=-16\\y=-48\end{matrix}\right.\) (loai)
x + 5 = 121 <=> \(\left\{{}\begin{matrix}x=116\\y=96\end{matrix}\right.\) (nhan)
x + 5 = -121 <=> \(\left\{{}\begin{matrix}x=-126\\y=-148\end{matrix}\right.\) (loai)
Vay (x;y) = (116;96)
