Question

[Xoxo Sehun]

Tìm cặp số nguyên (x,y) TM 
\(\frac{x}{8}-\frac{1}{y}=\frac{1}{4}\)

Answer 1

[soyeon_Tiểu bàng giải]

\(\frac{x}{8}-\frac{1}{y}=\frac{1}{4}\)

=> \(\frac{xy-8}{8y}=\frac{1}{4}\)

=> (xy - 8).4 = 8y

=> xy - 8 = 2y

=> xy - 2y = 8

=> y.(x - 2) = 8

Ta có bảng sau:

x - 2	1	-1	2	-2	4	-4	8	-8
y	8	-8	4	-4	2	-2	1	-1
x	3	1	4	0	6	-2	10	-6

Answer 2

[Sherlockichi Kazukosho]

\(\frac{x}{8}-\frac{1}{y}=\frac{1}{4}\)

\(\frac{xy}{8y}-\frac{8}{8y}=\frac{1}{4}\)

\(\frac{xy-8}{8y}=\frac{1}{4}\)

\(\Rightarrow4.\left(xy-8\right)=8y\)

\(\Rightarrow4xy-32=8y\)

\(32=4xy-2.4y\)

\(32=4y\left(x-2\right)\)

\(8=y\left(x-2\right)\)