Question
The difference between a positive proper fraction and its reciprocal is `9/20`. The fraction is :
Answer: Option C
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Let the required fraction be `x`. Then , `1/x` - `x` = `9/20`
`therefore` ` (1-x^2)/(x)` = `9/20` `rArr` 20 - `20x^2` = `9x` `rArr` `20x^2` + `9x` - 20 = 0
` rArr` 20`x^2` + 25`x` - 16`x` - 20 = 0 `rArr` 5`x` (4`x` + 5) - 4(4`x` + 5 ) = 0
`rArr` (4`x` + 5 ) (5`x` - 4 ) = 0 `rArr` `x` = `4/5`.
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