The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is-

Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is-Solution:Let the required fraction be x.Then,1/x - x =9/20⇒ (1 - x2)/x = 9/20⇒ 20 - 20x2 = 9x⇒ 20x2 + 9x - 20 = 0⇒ 20x2 + 25x - 16x - 20 = 0⇒ 5x(4x + 5) - 4(4x + 5) = 0⇒ (4x + 5)(5x - 4) = 04x + 5 = 0 or 5x - 4 = 0⇒ x = - 5/4 or x = 4/5 [x = - 5/4 not acceptable]∴ x = 4/5