Question

The sum of a natural number and its reciprocal is 65/8.Find the natural number

Answer 1

hence, the required number is 8

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Answer 2

let the no. be x

reciprocal will be 1

x

so, x + 1 / x = 65

8

x2 + 1 = 65

x 8

8x2 + 8 = 65x

8x2 - 65x + 8 = 0

8x2 - 64x - x + 8 = 0

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

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

x = 1

8

x = 8 ( bcz x is a natural no.)