Soviet Union Math Olympiad Problem | Can you solve it and find x and y | you should know this trick

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[SidneiMV]

(x + y) - xy = 1 => xy = (x + y) - 1
(x + y)² - xy = 7

x + y = b
xy = b - 1

b - 1 = b² - 7
b² - b - 6 = 0
(b - 3)(b + 2) = 0

x + y = b = 3
xy = 2
t² - 3t + 2 = 0
t = (3 ± 1)/2 => t = 2 ∨ t = 1

x + y = b = -2
xy = -3
t² + 2t - 3 = 0
t = (-2 ± 4)/2 => t = 1 ∨ t = -3

*(x, y) = {(1, 2); (2, 1); (1, -3); (-3, 1)}*

[deryakuru]

This question is hard for me, but easy for Soviet olimpiads :) and olimpiad students