Решите систему уравнений
2x^2 + xy - y^2 =20
x^2 - 4xy + 7y^2 = 13

2x^2 + xy - y^2 =20   |*13

x^2 - 4xy + 7y^2 = 13 |*-20

x, y ≠ 0

26x^2 + 13xy - 13y^2 =260  

-20x^2 + 80xy - 140y^2 = -260

Складываем

6x^2 + 93xy - 153y² = 0  | :y²

6(x/y)² + 93x/y - 153 = 0

x/y = t

6t² + 93t - 153 = 0

D = 93² + 4*6*153 = 12321 = 111²

t12 = (-93 +- 111)/12 = -17     3/2

1. x/y = -17

x = -17y

2x^2 + xy - y^2 =20

2(-17y)^2 + y*(-17y) - y^2 = 20

560y^2 = 20

y^2 = 1/28

y1 = √1/28 = √7/14

x = -17y

x1 = -17√7/14

y2 = -√7/14

x2 = 17√7/14

2. x/y = 3/2

2x^2 + xy - y^2 =20

2(3/2y)^2 + y*3/2y - y^2 = 20

9/2y^2 + 3/2y^2 - y^2 = 20

5y^2 = 20

y^2 = 4

y3 = 2

x3 = 3

y4 = -2

x4 = -3

ответ (3,2)(-3,-2)( -17√7/14, √7/14) (17√7/14, -√7/14)