Question

The sum of a number and its reciprocal is 17/4. Find the number.

Answer 1

Let the number be ‘x’

According to the given hypothesis

`x+1/x=17/4`

`rArr(x^2+1)/x=17/4`

⇒ 4(𝑥² + 1) = 17𝑥

⇒ 4𝑥² - 17𝑥 + 4 = 0

⇒ 4𝑥² - 16𝑥 - 𝑥 + 4 = 0

⇒ 4𝑥(𝑥 - 4) - 1(𝑥 - 4) = 0

⇒ 𝑥 =1/4 𝑜𝑟 𝑥 = 4

∴ The value of 𝑥 = 4