Question

The denominator of a fraction is one more than twice the numerator. If the sum of fraction and its reciprocal is 58/21. Find the fraction? [Solve using Quadratic Formula]
~ Quadratic Equations

Answer 1

Here is your required answer...

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the numerator of the fraction be x.

Then, its denominator of the fraction be (2x + 1).

Fraction = x/(2x + 1)

Reciprocal = (2x + 1)/x

According to the Question,

⇒ x/(2x + 1) + (2x + 1)/x = 58/21

⇒ 21[x² + (2x + 1)²] = 58x(2x + 1)

⇒ 21[5x² + 4x + 1] = 116x² + 58x

⇒ 11x² - 26x - 21 = 0

⇒ 11x² - 33x + 7x - 21 = 0

⇒ 11x(x - 3) + 7(x - 3) = 0

⇒ (x - 3) (11x + 7) = 0

⇒ x - 3 = 0 or 11x + 7 = 0

⇒ x = 3, - 7/11 (As x can't be negative)

⇒ x = 3

Numerator = x = 3

Denominator = 2x + 1 = 2(3) + 1 = 6 + 1 = 7

Fraction = 3/7

Hence, the required fraction is 3/7.