xy = -1 x + y = 2 x + y = -2 - x - x y = -x - 2 xy = -1 x(-x + 2) = -1 x(-x) + x(2) = -1 -x² + 2x = -1 + 1 + 1 -x² + 2x + 1 = 0 -1(x²) - 1(-2x) - 1(-1) = 0 -1(x² - 2x - 1) = 0 -1 -1 x² - 2x - 1 = 0 x = -(-2) ± √((-2)² - 4(1)(-1)) 2(1) x = 2 ± √(4 - 4(-1)) 2 x = 2 ± √(4 + 4) 2 x = 2 ± √(8) 2 x = 2 ± 2√(2) 2 x = 1 ± √(2) x + y = 2 (1 ± √(2)) + y = 2 - (1 ± √(2)) - (1 ± √(2)) y = 1 ± √(2) (x, y) = (1 ± √(2), 1 ± √(2)) The numbers that multiply to -1 and add to 2 are 1 ± √(2).
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