Question

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

Answer 1

Answer:

the numbers are 5 and 3

Step-by-step explanation:

Let the two numbers be a,b such that a+b=8 (given)

1/a+1/b=8/15

⇒(a+b)÷ab =8/15⇒ab =15

now (a+b)^2 = a^2+b^2+2ab

a^2+b^2=(8)^=2(15)

a^2+b^2=34

using this a^2+b^2 value in (a-b)^2 we get a-b =2

on solving a+b=8 and a-b=2 we get a=5 and b=3