tìm x,y biết:3x ²+xy-2y ²=2

Ta có: `3x^2 + xy - 2y^2 = 2`

`<=> 3x^2 + 3xy - 2xy - 2y^2 = 2`

`<=> 3x(x + y) -2y(x + y) = 2`

`<=> (3x - 2y)(x + y) = 2`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{3x - 2y}&\text{1}&\text{-1}&\text{2}&\text{-2}\\\hline \text{x + y}&\text{2}&\text{-2}&\text{1}&\text{-1}\\\hline \text{x}&\text{1}&\text{-1}&\text{$\dfrac{4}{5}$}&\text{$\dfrac{-4}{5}$}\\\hline \text{y}&\text{1}&\text{-1}&\text{$\dfrac{1}{5}$}&\text{$\dfrac{-1}{5}$}\\\hline \text{Kết luận}&\text{thỏa mãn}&\text{thỏa mãn}&\text{loại}&\text{loại}\\\hline\end{array}

Vậy `(x,y) \in {(1,1);(-1,-1)}`

$#duong612009$