Q79 of 134 Page 4


The denominator of a fraction is one more than twice the numerator. If the sumof the fraction and its reciprocal is 2https://static.philoid.co/ncertusercontent/solutions/user_files/63094/15042/images/extra-4_files/Image1280.gif , findthe fraction.


Let the numerator of the fraction be x.
Then the denominator of the fraction is 2x + 1.
The required fraction is .

21(5x 2 + 4x + 1) = 58(2x 2 + x)
105x 2 + 84x + 21 = 116x 2 + 58x
11x 2 - 26x - 21 = 0
11x 2 - 33x + 7x - 21 = 0
11x(x – 3) + 7(x – 3) = 0
(11x + 7)(x – 3) = 0
11x + 7 = 0 or x – 3 = 0
The required fraction is

Checking:

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