Math Olympiad | A Nice Algebra Problem | A Nice Math Problem

[@key_board_x]

@ 2:27 / 13:19 → faster by substitution
1 * 91
x² + xy + y² = 91 → where: x - y = 1 → y = x - 1
x² + x.(x - 1) + (x - 1)² = 91
x² + x² - x + x² - 2x + 1 = 91
3x² - 3x = 90
x² - x = 30
x² - x - 30 = 0
Δ = (1)² - (4 * - 30) = 1 + 120 = 121 = 11²
x = (1 ± 11)/2
x = - 5 → y = - 6
x = 6 → y = 5
7 * 13
x² + xy + y² = 13 → where: x - y = 7 → y = x - 7
x² + x.(x - 7) + (x - 7)² = 13
x² + x² - 7x + x² - 14x + 49 = 13
3x² - 21x + 36 = 0
x² - 7x + 12 = 0
Δ = (- 7)² - (4 * 12) = 49 - 48 = 1
x = (7 ± 1)/2
x = 4 → y = - 3
x = 3 → y = - 4

[@SALogics]

Great! ❤