{x² +y²+xy =7 ; x+y +xy =5 . {(x +y)² -xy =7 ; (x+y)+ xy =5.
(x +y)² -xy+(x+y)+ xy = 7+5;
(x+y)² +(x+y) -12 =0;
(x+y) = - 4 ;
(x+y) =3;
a) x+y = - 4 ;
x+y+xy =5;
-4 + xy =5;
xy =9;
{x+y = -4; xy = 9. {y = -4 -x ; x(-x - 4) =9.
x² +4x +9 =0 не имеет решения .
b) x+y =3 ;
x+y +xy =5;
3+xy =5 ;
xy =2;
{x + y =3; xy = 2. x=1 ;y =2 или x=2 ;y =1.
{y = 3 - x ; x(3-x) =2.
x(3-x) =2;
3x - x² = 2;
x² - 3x +2 =0 ;
x₁=1;
x₂=2.
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y₁ =3 -x₁= 3-1=2;
y₂ =3 -x₂ =3 -2 =1.
ответ : (1; 2) (2 ; 1) .