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Verified answer

Пусть a = x + y; b = x - y.

a² - 4a = 45
a² - 4a - 45 = 0
a² - 4a + 4 - 49 = 0
(a - 2)² - 7² = 0
(a - 2 - 7)(a - 2 + 7) = 0
(a - 9)(a + 5) = 0
a = 9 или a = -5
x + y = 9 или x + y = -5

b² - 2b = 3
b² - 2b - 3 = 0
b² - 2b + 1 - 4 = 0
(b - 1)² - 2² = 0
(b - 1 - 2)(b - 1 + 2) = 0
(b - 3)(b + 1) = 0
b = 3 или b = -1
x - y = 3 или x - y = -1

Решаем четыре системы:
1)
x + y = 9
x - y = 3

2x = 12
x + y = 9

x = 6
y = 3

2) 
x + y = 9
x - y = -1

2x = 8
x + y = 9

x = 4
y = 5

3) 
x + y = -5
x - y = 3

2x = -2
x + y = -5

x = -1
y = -4

4)
x + y = -5
x - y = -1

2x = -6
x + y = -5

x = -3
y = -2

Ответ: (-3; -2), (-1; -4),  (4; 5), (6; 3).