Question

[VUX NA]

Tìm các cặp số nguyên dương thỏa mãn 6x + 5y + 18 = 2xy

Answer 1

[Nguyễn Hoàng Minh]

\(6x+5y+18=2xy\\ \Leftrightarrow2xy-6x+15-5y=33\\ \Leftrightarrow2x\left(y-3\right)-5\left(y-3\right)=33\\ \Leftrightarrow\left(2x-5\right)\left(y-3\right)=33\)

Ta có:

\(2x-5\)	±33	±1	±3	±11
\(y-3\)	±1	±33	±11	±3
\(x\)	19;-14	3;2	4;1	8;-3
\(y\)	4;2	36;-30	14;-8	6;0

Vậy \(\left(x;y\right)=\left\{\left(19;4\right);\left(-14;2\right);\left(3;36\right);\left(2;-30\right);\left(4;14\right);\left(1;-8\right);\left(8;6\right);\left(-3;0\right)\right\}\)