sum of two natural numbers is eight and sum of their reciprocals is 8/15. find the two numbers?

let the no. be x and y

x+y=8 .......(1)

 

1/x + 1/y=8/15 ................(2)

i.e. (x+y)/(x*y) = 8/15

i.e x*y = 15 .......(put x+y=8 from 1)

i.e y=15/x........(3)

put (3) in (1) to get (x^2)-8x+15=0

solve to get x=3&y=5 or x=5&y=3

so the no. are 3 & 5

let 1 no =x

----2----=y

x+y=8            ------eg. 1 

   ;     1/x+1/y  = 8/15  i.e (x+y)/xy=8/15  

thus xy=15   now from eq.1, x=8-y putting here in this eq.

(8-y)*y=15

8y-y²=15    =    y²-8y+15=0

solving we get y=5 or y=3

so nos. are 5,3

Let no. be x and yX+y=8. -------------11/x +1/y =8/15X+y/x*y =8/15. --------------2( xy=15 and from equation 1 x=8-y)X*y=15Substituting (8-y)*y=15y-y^2 =15 y2-8y+15=0(y-3) (y-5)=0y=3 y=5We know that x+y=8When y=5,x=3When y=3,x=5