Question

Tìm các cặp số nguyên x,y thỏa mãn 

    \(\frac{x}{4}-\frac{1}{y}=\frac{3}{4}\)

Answer 1

\(\frac{x}{4}-\frac{1}{y}=\frac{3}{4}\)

\(\frac{1}{y}=\frac{x-3}{4}\)

\(\left(x-3\right)\times y=4=\left(-1\right)\times\left(-4\right)=\left(-4\right)\times\left(-1\right)=4\times1=1\times4=2\times2=\left(-2\right)\times\left(-2\right)\)

Vậy \(\left(x;y\right)\in\left\{\left(2;-4\right);\left(-1;-1\right);\left(7;1\right);\left(4;4\right);\left(5;2\right);\left(1;-2\right)\right\}\)

Answer 2

\(\frac{x}{4}\)-\(\frac{1}{y}\)=\(\frac{3}{4}\)

\(\frac{1}{y}\)=\(\frac{x-3}{4}\)

\(\Rightarrow\)y.(x-3)=4 hay y và x-3 \(\in\)Ư(4)

Ta có bảng sau:

y	1	-1	2	-2	4	-4
x-1	4	-4	2	-2	1	-1
x	5	-3	3	-1	2	0

Vậy (x;y)\(\in\){(5;1);(-3;-1);(3;2);(-1;-2);(2;4);(0;-4)}