Question

the sum of a natural number and its reciprocal is 65/8 find the number ​

Answer 1

let required no. be x

and, reciprocal be 1/x.

according to question,

x + 1/x = 65/8

x^2 + 1/ x = 65/8

8x^2 - 65x + 8 = 0

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

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

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

thus, the no. can be either 1/8 or 8.