Question

The sum of 2 natural numbers is 8 . find the numbers if their sum of their reciprocals is 8/15

Answer 1

let the two natural number be x and y then
according to the question x+y=8
and 1/x+1/y=8/15
solving above equation we get x+y/xy=8/15
now we know x+y=8. substitute this in above equation ,we get
8/xy=8/15
then xy = 15......(1)
x+y=8=> x=8-y out this in equation (1)
8y-y^2=15
y^2-8y+15=0
(y-3)(y-5)
hence there are two values of y putting it in equation (1) we get x=5,3
hence the values of x and y are 5,3