Question
The difference between a positive proper fraction and its reciprocal is \(\frac{9}{20}\) .The fraction is:
Answer: Option C
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Let the required fraction be x. Then \(\frac{1}{x}-x = \frac{9}{20}\)
Therefore \(\frac{1-x^{2}}{x} = \frac{9}{20}\)
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
\(x = \frac{4}{5}\)
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