giải PTNNguyen : x^2 + 2xy + x +1 +3y = 15

`x^2 + 2xy + x +1 +3y = 15`

`⇔x^2 + 2xy + x +3y = 14`

`⇔x(x+1)=14-y(2x+3)`

`⇔x^2+x-14=-y(2x+3)`

`⇔`\begin{cases}x^2+x-14 \vdots y\\x^2+x-14 \vdots 2x+3 \end{cases}

`⇔`\begin{cases}x^2+x-14 \vdots y\\4x^2+4x-56 \vdots 2x+3 \end{cases}

`⇔`\begin{cases}x^2+x-14 \vdots y\\(2x+3)(2x-1)-53\vdots 2x+3 \end{cases}

`⇔53\vdots 2x+3`

`⇔2x+3∈Ư(53)`

`⇔2x+3={±1;±53}`

`⇔x={-28;-2;-1;25}`

`+)`với` x=-28`

`⇒y=14`

`+)`với` x=-2`

`⇒y=-12`

`+)`với` x=-1`

`⇒y=14`

`+)`với` x=25`

`⇒y=-12`