Đáp án: `(x, y) ∈ { (3,4) ; (1,-4) ; (4,2) ; (0,-2) ; (6,1) ; (-2,-1) }`
Giải thích các bước giải:
`x/4 = 1/y + 1/2`
`⇒ x/4 - 1/2 = 1/y`
`⇒ x/4 - 2/4 = 1/y`
`⇒ (x - 2)/4 = 1/y`
`⇒ (x - 2)y = 4`
Mà `x, y ∈ ZZ`
nên: `x - 2` ; `y ∈ Ư (4) = { ±1 ; ±2 ; ±4 }`
Ta có bảng:
$\begin{array}{|c|c|c|}\hline \text{x - 2}&\text{1}&\text{-1}&\text{2}&\text{-2}&\text{4}&\text{-4}\\\hline \text{x}&\text{3}&\text{1}&\text{4}&\text{0}&\text{6}&\text{-2}\\\hline \text{y}&\text{4}&\text{-4}&\text{2}&\text{-2}&\text{1}&\text{-1}\\\hline\end{array}$
Vậy `(x, y) ∈ { (3,4) ; (1,-4) ; (4,2) ; (0,-2) ; (6,1) ; (-2,-1) }`
