Question

The sum of any two natural numbers is 8.Find the numbers if the sum of their reciprocals is 8/15

Answer 1

Let the numbers be X and 8-x
1/x+1/8-x=8/15
=>8-x+x/(8-x)×x=8/15
=>8/8x-x^2=8/15
=>8x-x^2=15
=>x^2-8x+15=0
=>x^2-3x-5x+15=0
=>x (x-3)-5 (x-3)=0
=>(x-5)(x-3)=0
=>x=3
x=5

hence the numbers are 3 and 5