Question

The denominator of a fraction is one more than twice the numerator. If the sum of the
find the fraction.
16
21
[CBSE 2016]
fraction and its reciprocal is 2​

Answer 1

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MATHS

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 22116, find the fraction.

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ANSWER

Let the numerator of the fraction be x. 

Then Denominator=2x+1

Fraction =2x+1x

Reciprocal of the fraction =x2x+1

It is given that the sum fo the fraction and its reciprocal is 22116

∴2x+1x+x2x+1=22116

⇒x(2x+1)x2+(2x+1)2=2158⇒2x2+x5x2+4x+1=2158

⇒21(5x2+4x+1)=