Question

Tìm x,y nguyên dương thỏa mãn: \(4xy-3\left(x+y\right)=59\)

Answer 1

\(4xy-3\left(x+y\right)=59\Rightarrow16xy-12x-12y=59.4\)

\(\Rightarrow4x\left(4y-3\right)-3\left(4y-3\right)=59.4+9\)

\(\Rightarrow\left(4x-3\right)\left(4y-3\right)=245\)

Ta có bảng sau: 

4x-3	1	5	7	35	49	245
4y-3	245	49	35	7	5	1
x	1	2	5/2	19/2	13	62
y	62	13	19/2	5/2	2	1

Mà x,y nguyên dương

Vậy \(\left(x;y\right)\in\left\{\left(1;62\right),\left(2;13\right),\left(13;2\right),\left(62;1\right)\right\}\)