Question

the differance of two natural number is 5 and the differance of their reciprocals is 1/10. find the number

Answer 1

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)

∴ Two numbers are 10 and (10-5) = 5.