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Question
The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.
Solution
Let the required fraction be `x/(2x + 1)`
From the given information,
`x/(2x + 1) + (2x + 1)/x = 2.9`
`(x^2 + 4x^2 + 1 + 4x)/(x(2x + 1)) = 29/10`
`(5x^2 + 1 + 4x)/(2x^2 + x) = 29/10`
`50x^2 + 10 + 40x = 58x^2 + 29x`
`8x^2 - 11x - 10 = 0`
`x = (11 +- sqrt(121 + 320))/16`
`x = (11+-sqrt441)/16`
`x = (11 +- 21)/16`
`x = 2, -5/8`
Thus, the required fraction is `2/5`
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