Question

Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Answer 1

Given that the sum of two numbers is 16.

Let the two numbers be x and 16 - x

By the given hypothesis, we have

`rArr1/x+1/(16-x)=1/3`

`rArr(16-x+x)/(x(16-x))=1/3`

⇒ 48 = 16x - x²

⇒ 𝑥² - 16𝑥 + 48 = 0

⇒ 𝑥2 - 12𝑥 - 4𝑥 + 48 = 0

⇒ x(x - 12) - 4(x - 12) = 0

⇒ (x - 12) (x - 4) = 0

⇒ x = 12 or x = 4

∴ The two numbers are 4 and 12.