Question

the sum of a natural number a d its reciprocal is 65/8. find the natural no. plz ans ASAP

Answer 1

let the natural number ia r and its reciprocal is hence 1/r so as per question
r+1/r= 65/8

Answer 2

Let the natural number be x.

Given that sum of a natural number and it reciprocal is 65/8.

x + 1/x = 65/8

$\frac{x^2 + 1}{x} = \frac{65}{8}$

8x^2 + 8 - 65x = 0

8x^2 - 65x + 8 = 0

8x^2 - 64x - x + 8 = 0

8x(x - 8) - 1(x - 8) = 0

(8x - 1)(x - 8) = 0

x = 1/8,8.


Therefore the natural number is 8 or 1/8. If we want an integer then x = 8.


Verification:

8 + 1/8 = 65/8

65/8 = 65/8


Hope this helps!