Question

Tìm các số nguyên dương x,y:

\(\frac{x}{2}+\frac{x}{y}-\frac{3}{2}=\frac{10}{y}\)

Answer 1

\(\frac{x}{2}-\frac{3}{2}=\frac{10}{y}-\frac{x}{y}\)

\(\frac{x-3}{2}=\frac{10-x}{y}\)

\(\Leftrightarrow\left(x-3\right)\cdot y=2\cdot\left(10-x\right)\)

\(xy-3y=20-2x\)

\(xy+2x-3y-6=14\)

\(x\left(y+2\right)-3\left(y+2\right)=14\)

\(\left(y+2\right)\left(x-3\right)=14\)

\(y+2\)	-1	1	-2	2	-7	7	-14	14
\(x-3\)	-14	14	-7	7	-2	2	-1	1
\(y\)	-3	-1	-4	0	-9	5	-16	12
\(x\)	-11	17	-4	10	1	5	2	4

Vậy các cặp (x;y) là: (-11;-3) (17;-1) (-4;-4) (10;0) (1;-9) (5;5) (2;-16) (4;12)