a: =>\(\dfrac{xy-6}{6y}=\dfrac{1}{2}\)
=>xy-6=3y
=>y(x-3)=6
=>\(\left(x-3;y\right)\in\left\{\left(1;6\right);\left(6;1\right);\left(-1;-6\right);\left(-6;-1\right);\left(2;3\right);\left(3;2\right);\left(-2;-3\right);\left(-3;-2\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(4;6\right);\left(9;1\right);\left(2;-6\right);\left(-3;-1\right);\left(5;3\right);\left(6;2\right);\left(1;-3\right);\left(0;-2\right)\right\}\)
b: \(\Leftrightarrow\dfrac{20+xy}{4x}=\dfrac{1}{8}\)
=>20+xy=1/2x
=>40+2xy=x
=>x-2xy=40
=>x(1-2y)=40
=>x(2y-1)=-40
mà x,y nguyên
nên \(\left(x;2y-1\right)\in\left\{\left(40;-1\right);\left(-40;1\right);\left(8;-5\right);\left(-8;5\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(40;0\right);\left(-40;1\right);\left(8;-2\right);\left(-8;3\right)\right\}\)
d: =>(xy-4)/4y=3/4
=>xy-4=3y
=>y(x-3)=4
=>\(\left(x-3;y\right)\in\left\{\left(1;4\right);\left(4;1\right);\left(-1;-4\right);\left(-4;-2\right);\left(2;2\right);\left(-2;-2\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(4;4\right);\left(7;1\right);\left(2;-4\right);\left(-1;-2\right);\left(5;2\right);\left(1;-2\right)\right\}\)
