Question

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

Answer 1

Let the number be x
Since sum of a number and its reciprocal is 65/8 so we have
x+1/x=65/8
8x^2+8=65x
8x^2-65x+8=0
8x^2-64x-x+8=0
8x(x-8)-1(x-8)=0
(8x-1)(x-8)=0
x=8,1/8
So the numbers are 8 or 1/8

Answer 2

hi 
let x is number and 1/x is reciprocal of number
 now 
      x+1/x = 65/8
solved the question, we get
x²+1=65x/8
8x²+8=65x
8x-65x+8=0
solve by quardic eqation
we get 
x= 1/8 and  x=1