Question

Tìm các số nguyên x , y biết rằng :

\(\frac{x}{4}-\frac{1}{y}=\frac{1}{2}\)

Answer 1

\(\frac{x}{4}-\frac{1}{y}=\frac{1}{2}\)

\(\frac{x}{4}-\frac{1}{2}=\frac{1}{y}\)

\(\frac{x}{4}-\frac{2}{4}=\frac{1}{y}\)

\(\frac{x-2}{4}=\frac{1}{y}\)

\(y\left(x-2\right)=4\)

       Ta có:4=2.2=(-2).(-2)=4.1=1.4=(-1).(-4)=(-4).(-1)

    Do đó ta có bảng sau:

y	4	1	2	-2	-4	-1
x-2	1	4	2	-2	-1	-4
x	3	6	4	0	1	-2

       Vậy cặp (x;y) TM là:(3;4)(6;1)(4;2)(0;-2)(1;-4)(-2;-1)

Answer 2

\(\frac{x}{4}-\frac{1}{y}=\frac{1}{2}\\ \Rightarrow\frac{xy}{4y}-\frac{4}{4y}=\frac{1}{2}\\ \Rightarrow\frac{xy-4}{4y}=\frac{1}{2}\\ \Rightarrow2\left(xy-4\right)=4y\\ \Rightarrow2xy-8=4y\\ \Rightarrow2xy-4y-8=0\\ \Rightarrow y\left(2x-4\right)=8\)

2x-4	1	8	2	4	-1	-8	-2	-4
y	8	1	4	2	-8	-1	-4	-2
x		6	3	4		-2	1	0

 

Vậy (x;y)=(6;1);(3;4);(4;2);(-2;-1);(1;-4);(0;-2)