Question

The sum of natural no. And its reciprocal is 65/8. Find the natural no. Plzz hlp

Answer 1

Heya!

Let us find the answer:

Solution:

Let the Number be k,

It's reciprocal is 1/k .

⇒ k + 1/k = 65/8

⇒ k² + 1/k = 65/8

⇒ 8k² + 8 = 65k

⇒ 8k² + 8 - 65k = 0

⇒ 8k² - 64k - k + 8 = 0

⇒ 8k(k - 8) - 1(k - 8) = 0

⇒ 8k - 1(k - 8) = 0

⇒ 8k - 1 = 0

⇒ 8k = 1

⇒ k = 1/8

⇒ k - 8=0

⇒ k = 8

Hence, the number is 8 or 1/8.