x^2 + y^2 = 20

xy = -6

.

(-6/y)^2 + y^2 = 20

x = -6/y

.

36/y^2 + y^2 = 20

x = -6/y

.

36 + y^4 = 20y^2

x = -6/y

.

Пусть t=y^2, тогда

36 + t^2 = 20t

x = -6/y

.

36 + t^2 - 20t = 0

x = -6/y

.

D = 400 - 144 = 256

t1 = (20 + √256) / 2 = 18

t2 = (20 - √256) / 2 = 2

.

t = y^2, значит

y^2 = 18

y = +-√18

y^2 = 2

y = +-√2

.

В итоге у нас получилось 4 системы

y = √18

x = -6/√18

.

y = -√18

x = 6/√18

.

y = √2

x = -6/√2

.

y = -√2

x = 6/√2

.

Задание 2:

x^2 + y^2 = 36

-x^2 + y = 6

.

x^2 + y^2 = 36

y^2 + y = 42

.

x^2 + y^2 = 36

y^2 + y - 42 = 0

.

D = 1 + 168 = 169

y1 = (-1 + √169)/ 2 = 6

y2 = (-1 - √169)/2 = -7

.

x^2 + 6^2 = 36

y = 6

.

x = 0

y = 6

.

x^2 + (-7)^2 = 36

y = -7

пустое множество.

Ответ: (0;6), (∅; -7)

Задание 3.

1/x - 1/y = 2

1/x^2 - 1/y^2 = 16

.

Пусть t = 1/x, z = 1/y, тогда

t - z = 2

t^2 - z^2 = 16

.

t = 2 + z

(2+z)^2 - z^2 = 16

.

t = 2 + z

4 + 4z + z^2 - z^2 = 16

.

t = 2 + z

4z = 12

.

t = 5

z = 3

.

5 = 1/x

3 = 1/y

.

Ответ:

x = 1/5

y = 1/3