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The Denominator of a Fraction is One More than Twice the Numerator. If the Sum of the Fraction and Its Reciprocal is 2.9; Find the Fraction - Mathematics

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Question

The denominator of a 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`

`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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 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(A) | Q: 10 | Page no. 70
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Solution The Denominator of a Fraction is One More than Twice the Numerator. If the Sum of the Fraction and Its Reciprocal is 2.9; Find the Fraction Concept: Quadratic Equations.
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