Question

Tìm các căp số nguyên dương (a,b) biết 3a-b+ab=8

Answer 1

\(3a-b+ab=8\\ \Rightarrow a\left(3+b\right)-b-3=8-3\\ \Rightarrow a\left(b+3\right)-\left(b+3\right)=5\\ \Rightarrow\left(b+3\right)\left(a-1\right)=5\)

Vì \(a,b\in N\Rightarrow\left\{{}\begin{matrix}a-1\in Z,b+3\in N,b+3\ge3\\a-1,b+3\inƯ\left(5\right)\end{matrix}\right.\)

Ta có bảng:

a-1	1
b+3	5
a	2
b	2

Vậy \(\left(a,b\right)\in\left\{\left(2;2\right)\right\}\)