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)}*

[@deryakuru6548]

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

[@2sljmath]

👍🏻