Tìm các số tự nhiên x,y sao cho:x/9-3/y=1/18

Cai bang nhin gom vai o

`x/9-3/y=1/18=>x/9=1/18+3/y=\frac{y+54}{18y} `

`=>x.18y=9.(y+54)`

`=>2xy=x+54(**)`

Vì `2xy \vdots y,y \vdots y`,nên từ `(**)=>54 \vdots y`

`=>x in Ư(54)={1;2;3;6;18;9;27;54}`

{|1|2|3|4|5|6|7|8|9|}\hline\text{y}&\text{1}&\text{2}&\text{3}&\text{6}&\text{9}&\text{18}&\text{27}&\text{54}\\\hline\text{}&\text{}&\text{}\\\hline\text{2xy}&\text{2x}&\text{4x}&\text{6x}&\text{12x}&\text{18x}&\text{36x}&\text{54x}&\text{108x}\\\hline\text{y}&\text{55}&\text{56}&\text{60}&\text{63}&\text{72}&\text{81}&\text{108}\\\hline\text{x}&\exists&\text{14}&\exists&\text{5}&\exists&\text{2}&\exists&\text{1}\\\hline\end{array}

Vậy có các cặp số tự nhiên `(x;y)` thỏa mãn bài ra là:`(x;y)in{14;2);(5;6);(2;18);(1;54)}`