решите систеу уравнений {x^2+2xy+y^2=1 {x^2-xy-4y^2=2

Question

решите систеу уравнений {x^2+2xy+y^2=1 {x^2-xy-4y^2=2

Answer 1

{x^2+2xy+y^2=1
{x^2-xy-4y^2=2
***************
{x^2+2xy+y^2=1
{x^2-xy-4y^2=2x^2+4xy+2y^2
***************
{x^2+2xy+y^2=1
{x^2+5xy+6y^2=0
***************
{(x+y)^2=1
{(x+2y)(x+3y)=0
***************
x=-2y (y-2y)^2=1 y=(+/-)1 x=(-/+)2
или
x=-3y (y-3y)^2=1 y=(+/-)1/2 x=(-/+)3/2

ответ (-2;1);(2;-1);(-3/2;1/2);(3/2;-1/2)