Question

[BRUH]

Tìm các số nguyên x y , sao cho 5/x + y/3= 1/6

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\dfrac{5}{x}+\dfrac{y}{3}=\dfrac{1}{6}\)

=>\(\dfrac{15+xy}{3x}=\dfrac{1}{6}\)

=>\(\dfrac{30+2xy}{6x}=\dfrac{x}{6x}\)

=>\(x=2xy+30\)

=>x-2xy=30

=>x(1-2y)=30

=>x(2y-1)=-30

mà 2y-1 lẻ

nên \(x\left(2y-1\right)=30\cdot\left(-1\right)=\left(-30\right)\cdot1=2\cdot\left(-15\right)=\left(-2\right)\cdot15=10\cdot\left(-3\right)=\left(-10\right)\cdot3=6\cdot\left(-5\right)=\left(-6\right)\cdot5\)

=>\(\left(x;2y-1\right)\in\left\{\left(30;-1\right);\left(-30;1\right);\left(2;-15\right);\left(-2;15\right);\left(10;-3\right);\left(-10;3\right);\left(6;-5\right);\left(-6;5\right)\right\}\)

=>\(\left(x;y\right)\in\left\{\left(30;0\right);\left(-30;1\right);\left(2;-7\right);\left(-2;8\right);\left(10;-1\right);\left(-10;2\right);\left(6;-2\right);\left(-6;3\right)\right\}\)