Question

[abcde]

có bnh cặp số nguyên (x;y) thỏa mãn:

x/3 + 1/6 = -1/y

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\dfrac{x}{3}+\dfrac{1}{6}=\dfrac{-1}{y}\)

=>\(\dfrac{2x+1}{6}=\dfrac{-1}{y}\)

=>y(2x+1)=-6

mà 2x+1 lẻ

nên \(\left(2x+1\right)\cdot y=1\cdot\left(-6\right)=\left(-1\right)\cdot6=3\cdot\left(-2\right)=\left(-3\right)\cdot2\)

=>\(\left(2x+1;y\right)\in\left\{\left(1;-6\right);\left(-1;6\right);\left(3;-2\right);\left(-3;2\right)\right\}\)

=>\(\left(x;y\right)\in\left\{\left(0;-6\right);\left(-1;6\right);\left(1;-2\right);\left(-2;2\right)\right\}\)