Question

sum of two integers is 10 and the sum of their reciprocal is 5/12. find the integers

Answer 1

let x and y be 2 integers

x+y=10----------->1 and (1/x)+(1/y)=5/12------------>2

from 2 we get (x+y)/xy=5/12

i.e, 12(x+y)=5xy

from 1 we get x+y=10

5xy=120

xy=24

from this we get x=24/y----------->3

on substituting this equation in x+y=10 we get (24/y)+y=10

from this we get y²-10y+24=0

hence we will get y=6      or        y=4

if y=6 then x=4

if x=4 then y=6

hence these 2 integers are 6 and 4

Answer 2

This is a formal answer as examination point of view and if the chapter is algebraic identities.