`4x^2+9y^2=1987+13xy`

`=> 4x^2-13xy+9y^2=1987`

`=> 4x^2-4xy-9xy+9y^2=1987`

`=> 4x(x-y)-9y(x-y)=1987`

`=> (4x-9y)(x-y)=1987`

Vì `x,y \in ZZ => 4x-9y;x-y \in ZZ` nên ta có các TH sau:

`TH1:`

`{(4x-9y=1987),(x-y=1):}=>``{(4x-9y=1987),(4x-4y=4):}`

`=> 4x-9y-4x+4y=1987-4` `=> -5y=1983` `=> y=-1983/5` (loại)

`TH2:`

`{(4x-9y=-1987),(x-y=-1):}=>``{(4x-9y=-1987),(4x-4y=-4):}`

`=> 4x-9y-4x+4y=-1987+4` `=> -5y=-1991` `=> y=-1991/5` (loại)

`TH3:`

`{(4x-9y=1),(x-y=1987):}=>``{(4x-9y=1),(4x-4y=7948):}`

`=> 4x-9y-4x+4y=1-7948` `=> -6y=-7947` `=> y=7947/4` (loại)

`TH4:`

`{(4x-9y=-1),(x-y=-1987):}=>``{(4x-9y=-1),(4x-4y=-7948):}`

`=> 4x-9y-4x+4y=-1+7948` `=> -6y=7947` `=> y=-7947/4` (loại)

Vậy không có `x,y` nào thỏa mãn