Question

The sum of the numerator and the denominator is 8 and their product is 15. Then the fraction is ______.

विकल्प

• \[\dfrac{5}{3}\] and \[\dfrac{3}{5}\]

• \[\dfrac{5}{3}\] or \[\dfrac{3}{5}\]

• 3 and 5

• 3 or 5

Answer 1

The sum of the numerator and the denominator is 8 and their product is 15. Then the fraction is `bbunderline(5/3) or bbunderline(3/5)`.

Explanation:

It is given that the sum of the numerator and the denominator is 8.

Let the numerator of the fraction be x. So, denominator of the fraction = 8 − x

And, the product of numerator and denominator is 15.

⇒ x(8 − x) = 15

⇒ 8x − x² = 15

⇒ 8x − x² − 15 = 0

⇒ x² − 8x + 15 = 0

⇒ x² − 5x − 3x + 15 = 0

⇒ x(x − 5) − 3(x − 5) = 0

⇒ (x − 5)(x − 3) = 0

⇒ (x − 5) = 0 or (x − 3) = 0

⇒ x = 5 or x = 3

When x = 5, denominator = 8 − 5 = 3

When x = 3, denominator = 8 − 3 = 5

So. the fraction = \[\dfrac{5}{3}\] or \[\dfrac{3}{5}\]