Question

the sum of two numbers is 9 and the sum of their reciprocal is 1/2 . find that numbers

Answer 1

Let the two numbers be X and Y

according to the question

x + y = 9 ----------- equation 1

x = 9 - y

1/x + 1/y = 1/2 ---------- equation 2

1/9-y + 1/y = 1/2

take a LCM

y + 9 - y / 9y - y² = 1/2

18 = 9y - y²

y² -9y + 18 = 0

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the 1st required natural number be x.

And the 2nd natural number be (9 - x).

Then,

According to the Question,

⇒ 1/x + 1/(9 - x) = 1/2

⇒ (9 - x) + x/x(9 - x) = 1/2

By cross multiplication, we get

⇒ x(9 - x) = 18

⇒ x² - 9x + 18 = 0

⇒ x² - 6x - 3x + 18 = 0

⇒ x(x - 6) - 3(x - 6) = 0

⇒ (x - 6) (x - 3) = 0

⇒ x - 6 = 0 or x - 3 = 0

⇒ x = 6, 3

1st Number = 6, 3

2nd Number = 3, 6

Hence, the required numbers are 6 and 3 or 3 and 6.