2x+y+sqrt (x^2-4y^2) = 2, x*sqrt (x^2-4y^2) = 0

1. Приравняем множители второго уравнения к нулю:

{2x + y + √ (x^2 - 4y^2) = 2;

{x√ (x^2 - 4y^2) = 0; {2x + y + √ (x^2 - 4y^2) = 2;

{[x = 0;

{[√ (x^2 - 4y^2) = 0.

2. Рассмотрим каждый случай:

1)

{2x + y + √ (x^2 - 4y^2) = 2;

{x = 0; {y + √ (-4y^2) = 2;

{x = 0; {y = 0;

{0 + √0 = 2;

{x = 0.

Нет решений.

2)

{2x + y + √ (x^2 - 4y^2) = 2;

{√ (x^2 - 4y^2) = 0; {2x + y = 2;

{ (x + 2y) (x - 2y) = 0; {2x + y = 2;

{x = ±2y.

a)

{2x + y = 2;

{x = - 2y; {-4y + y = 2;

{x = - 2y; {-3y = 2;

{x = - 2y; {y = - 2/3;

{x = 4/3.

b)

{2x + y = 2;

{x = 2y; {4y + y = 2;

{x = 2y; {5y = 2;

{x = 2y; {y = 2/5;

{x = 4/5.

Ответ: (4/3; - 2/3); (4/5; 2/5).