Question

The difference of the squares of two positive integers is 180. The square of the smaller
number is 8 times the larger, find the numbers.
(CBSE 2014)
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.​

Answer 1

2.let numbers be x,y

x+y=18

1/x+1/y=1/4

->x+y/xy=1/4

xy=72

we have (x-y).^2=(x+y).^2-4xy

(x-y).^2=36

x-y=6

x+y=18

so we get x=12,y=8