Question

The difference of two numbers is 5 and the difference of their reciprocals is 1/10. Find the numbers .

Answer 1

let the numbers be x and y
x - y = 5
1/x - 1/y = 1/10
x-y/xy = 1/10
so x-y=1
xy= 10
but x-y = 5
then xy = 5 × 10= 50
therefore x = 5 and y = 10
guess this will be clear and usefull

Answer 2

Answer:

Let the two numbers be x and x - 5 .

According to the question.

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0

⇒ x2 - 10x + 5x - 50 = 0

⇒ x (x - 10) + 5 (x - 10) = 0

⇒ (x+5) (x-10) = 0

⇒ (x+5) (x-10) = 0

⇒ x = -5 or 10

⇒ x = 10 (x = -5 , rejected)