The difference of two numbers is −9, and the sum of their squares is 41. Find a pair of numbers, which fits these criteria.

Answer 1

x - y = -9

x² + y² = 41

x² - 2xy + y² = 81

-2xy = 40

xy = -20

x(x + 9) = -20

x² + 9x + 20 = 0

(x + 4)(x + 5) = 0

(-4, 5), (-5, 4)