Question

The sum of two numbers is 9. The sum of their reciprocals is `1/2`. Find the numbers.

Answer 1

Let one numbers be x then other (9 - x).

Then according to question

`1/x + 1(9-x)=1/2`

`rArr((9-x)+x)/(x(9-x))=1/2`

`rArr9/(x(9-x))=1/2`

By cross multiplication

⇒ 18 = x(9 - x)

⇒ x² - 9x + 18 = 0

⇒ x² - 6x - 3x + 18 = 0

⇒ x(x - 6) - 3(x - 6) = 0

⇒ (x - 6)(x - 3) = 0

⇒ x - 6 = 0

⇒ x = 6

Or

⇒ x - 3 = 0

⇒ x = 3

Since, x being a number,

Therefore,

When x = 6 then

(9 - x) = (9 - 6) = 3

When x = 3 then

(9 - x) = (9 - 3) = 6

Thus, two consecutive number be either 3, 6 or 6, 3.