Question

[Khuyễn Miên]

1. Tìm x,y \(\inℤ\)biết rằng:

a) ( 5.x + 1 ) . ( y - 1 ) = 4

b) 5xy - 5x + y = 5

Answer 1

[Trần Tiến Pro ✓]

\(\text{a) }\left(5x+1\right)\left(y-1\right)=4\)

\(\Leftrightarrow5x+1,y-1\inƯ\left(4\right)\)

\(\Leftrightarrow5x+1,y-1\in\left\{\pm1;\pm2;\pm4\right\}\)

Ta có bảng :

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

\(\text{b) }5xy-5x+y=5\)

\(\Leftrightarrow\left(5xy+y\right)-5x=5\)

\(\Leftrightarrow y\left(5x+1\right)-\left(5x+1\right)-1=5-1\)

\(\Leftrightarrow y\left(5x+1\right)-\left(5x+1\right)-1=4\)

\(\Leftrightarrow\left(y-1\right).\left(5x+1\right)=4\)

\(\Leftrightarrow y-1,5x+1\inƯ\left(4\right)\)

\(\Leftrightarrow y-1,5x+1\in\left\{\pm1;\pm2;\pm4\right\}\)

Ta có bảng :

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