Question

Tìm tất cả các cặp số nguyên dương ( x; y ) thoả mãn: \(2x^2+2xy-x+y=66\)

Answer 1

\(\Leftrightarrow\left(x+y\right)\left(2x-1\right)=66\)

\(\Rightarrow x+y=\dfrac{66}{2x-1}\)\(\Rightarrow2x-1\inƯ\left(66\right)=\left\{1;2;3;6;11;12;18;66\right\}\)

\(\Rightarrow x\in\left\{1;2;6\right\}\) thỏa mãn.

\(\Rightarrow x+y\in\left\{66;22;6\right\}\)

*\(x+y=66\Rightarrow y=65\)(TM)

*\(x+y=22\Rightarrow y=20\)(TM)

*\(x+y=6\Rightarrow y=0\)(TM)

Vậy (x;y)=\(\left(1;65\right);\left(2;20\right);\left(6;0\right)\).