\(\dfrac{1}{x}+\dfrac{y}{3}=\dfrac{5}{6}\)
=>\(\dfrac{3+xy}{3x}=\dfrac{5}{6}\)
=>\(\dfrac{6+2xy}{6x}=\dfrac{5x}{6x}\)
=>5x=2xy+6
=>5x-2xy=6
=>x(5-2y)=6
=>\(\left(x;5-2y\right)\in\left\{\left(1;6\right);\left(6;1\right);\left(-1;-6\right);\left(-6;-1\right);\left(2;3\right);\left(3;2\right);\left(-2;-3\right);\left(-3;-2\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(1;-\dfrac{1}{2}\right);\left(6;2\right);\left(-1;\dfrac{11}{2}\right);\left(-6;3\right);\left(2;1\right);\left(3;\dfrac{3}{2}\right);\left(-2;4\right);\left(-3;\dfrac{7}{2}\right)\right\}\)
mà x,y nguyên
nên \(\left(x;y\right)\in\left\{\left(6;2\right);\left(-6;3\right);\left(2;1\right);\left(-2;4\right)\right\}\)
