Question

Tìm các số nguyên x,y biết :

a). \(\dfrac{x}{2}\)=\(\dfrac{-5}{y}\).                                  b). \(\dfrac{3}{x}\)=\(\dfrac{y}{4}\), trong đó x > y > 0.

c). \(\dfrac{3}{x-1}\)= y+1.                           d). \(\dfrac{x+2}{5}\)=\(\dfrac{1}{y}\).

Answer 1

a, \(\dfrac{x}{2}=-\dfrac{5}{y}\Rightarrow xy=-10\Rightarrow x;y\inƯ\left(-10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)

x	1	-1	2	-2	5	-5	10	-10
y	-10	10	-5	5	-2	2	-1	1

 

c, \(\dfrac{3}{x-1}=y+1\Rightarrow\left(y+1\right)\left(x-1\right)=3\Rightarrow x-1;y+1\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

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

 

Answer 2

b: =>xy=12

\(\Leftrightarrow\left(x,y\right)\in\left\{\left(12;1\right);\left(6;2\right);\left(4;3\right)\right\}\)