Question

The sum of two numbers is 11 and the sum of their reciprocals is 11/28. Find the number.

Answer 1

x + y = 11

1/x + 1/y = 11/28

1/x + 1/(11 - x) = 11/28

(11 - x + x)/(x(11 - x)) = 11/28

11x - x² = 28

x² - 11x + 28 = 0

(x - 7)(x - 4) = 0

x = 4, 7

The numbers are 4 and 7.