The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: Correct Answer 4/5
Let x be the required fraction then acc to Q we have, 1/x - x = 9/20 So, (1 - x^2)/x = 9/20 or, 20 - 20x^2 = 9x or, 20x^2 + 9x - 20 = 0 or, 20x^2 - 25x - 16x - 20 = 0 or, 5x(4x + 5) - 4(4x + 5) = 0 ∴ (5x - 4) (4x + 5) = 0 so, (5x - 4) = 0 or, (4x + 5) = 0 or, x = 4/5 ∴x = - 5/4 [ not acceptable, as x cannot be negative] Hence, x = 4/5 (ans)