Question

the denominator of a fraction is one more than twice the numerator if the sum of fraction and its reciprocal is 2 16/21 find the fraction

Answer 1

Answer:

Step-by-step explanation:

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

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Answer 2

Answer:

Step-by-step explanation:

Correct Question :-

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2(16/21), find the fraction.

Answer :-

Solution :-

Let the numerator be x.

And the fraction = x/2x + 1

According to the Question,

Again x/2x + 1 + 2x + 1/x = 58/21

⇒ x² + (2x - 1)²/x(2x + 1) = 58/21

⇒ 5x² + 4x + 1/2x² + x = 58/21

⇒ 21(5x² + 4x + 1) = 58(2x² + x)

⇒ 105x² + 84x + 21 = 116x² + 58x

⇒ 11x² + 26x - 21 = 0

⇒ 11x² + 33x - 7x - 21 = 0

⇒ 11x(x + 3) + 7(x + 3) = 0

⇒ x = 3, - 7/11 (x can't be negative)

Hence, the required fraction is 3/7.