Question

the sum of a rational number and it's reciprocal is 13/6.find the number

Answer 1

let the no be x
x+1/x=13/6
(x^2+1)/x=13/6
x^2+1=13x/6
6(x^2+1)=13x
6x^2+6-13x=0
6x^2-13x+6=0
6x^2-4x-9x+6=0
2x(3x-2)-3(3x+2)=0
(2x-3)(3x-2)=0
hence 2x-3=0
2x=3
x=3/2 or
3x-2=0
3x=2 x=2/3

Answer 2

let 
x + 1/x = 13/6
x^2 +1  = 13
    x           6

6 x^2 + 6 = 13 x
6 x^2  - 13 x  + 6 =0
6 x^2 - 9 x - 4 x + 6 = 0
3 x( 2 x - 3) - 2 ( 2 x - 3) = 0
(2 x - 3) ( 3 x - 2) = 0
2 x - 3 = 0   &  3 x - 2 = 0
  x = 3/2 , 2/3
So the numbers are 3/2 & 2/3