Question

The sum of two numbers is 8and the sum of their reciprocals is 8/15 find the numbers

Answer 1

let a and b are two numbers ,
according to question,

a + b = 8 -------(1)

1/ a + 1/b =8/15

=> ( a + b)/ab =8/15

from equation (1)
8 /ab = 8/15
ab = 15
now,
equation (1)
a + b = 8
take square both side
a^2 +b^2 + 2ab = 64
(a -b)^2 +4ab =64
( a -b)^2 =64 -4ab =64 -4 × 15 =4
take square root
(a - b) = +_2
now ,
solve by use ,
(a -b) = +_ 2
& (a +b) =2

if (a -b) =2 then a =5 , and b =3
if ( a-b) = -2 then a =3 and b =5