Решите уравнение[latex] \left \{ {{(x-y)^{2}-x+y=o} \atop { x^{2}y^{2}-xy-2=o}} \right. [/latex]

Question

Решите уравнение[latex] \left \{ {{(x-y)^{2}-x+y=o} \atop { x^{2}y^{2}-xy-2=o}} \right. [/latex]

Алгебра

Решите уравнение [latex] \left \{ {{(x-y)^{2}-x+y=o} \atop { x^{2}y^{2}-xy-2=o}} \right. [/latex]

Гость

Ответ(ы) на вопрос:

Accepted Answer

[latex] \left \{ {{(x-y)^2-x+y=0} \atop {y^2-xy-2=0}} \right.\\ \\ x^2-2xy+y^2-x+y=y^2-xy-2\\ x^2-xy-x+y=-2\\ x(x-y)-(x-y)=-2\\ (x-y)(x-1)=-2\\ y=\frac{-2}{x-1}-x\\ (\frac{-2}{x-1}-x)^2-x*(\frac{-2}{x-1}-x)-2=0\\ x=-1\\ y=-2[/latex]