С две неизвестни

[Гост]

[tex]\begin{array}{|l} x^{2 } + 2x - 3 = xy + 3y \\ xy = 6 \end{array}[/tex]

[S.B.]

[tex]\begin{array}{|l} x^{2 } + 2x - 3 = xy + 3y \\ xy = 6 \end{array}[/tex]

[tex]x \ne 0 , y \ne 0[/tex]
[tex]\begin{array}{|l} x^{2 } + 2x- 3 = xy + 3y \\ xy = 6\end{array} \Leftrightarrow \begin{array}{|l} x^{2 } + 2x -3 = xy + 3y \\ y= \displaystyle \frac{6}{x} \end{array} \Leftrightarrow x^{2 } + 2x - 3 - 6 - \displaystyle \frac{18}{x} = 0 \Leftrightarrow[/tex]

[tex]x^{3 } + 2 x^{2 } - 9x - 18 = 0 \Leftrightarrow x^{2 }(x + 2) - 9(x + 2) = 0 \Leftrightarrow (x + 2)( x^{2 }- 9) = 0 \Leftrightarrow(x + 2)(x + 3)(x - 3) = 0[/tex]
$$(x_{1 } = - 2 , y_{1 } = - 3) ; (x_{2 } = - 3 , y_{2 } = -2) ; (x_{3 } = 3 , y_{3 } = 2)$$