Question

The sum of a number and its reciprocal is 17/4, Find the numbers.
1. 4 and 1/2
2. 3 and 1/3
3. 5 and 1/5
4. 4 and 1/4

Answer 1

Correct Answer - Option 4 : 4 and 1/4

Let the number be a.

According to question:

a + 1/a = 17/4

⇒ (a² + 1)/a = 17/4

⇒ 4(a² + 1) = 17a

⇒ 4a² + 4 = 17a

⇒ 4a² – 17a + 4 = 0

⇒ 4a² – (16 + 1)a + 4 = 0

⇒ 4a² – 16a – a + 4 = 0

⇒ 4a (a – 4) – 1(a – 4) = 0

⇒ (4a – 1) = 0 or (a – 4) = 0

⇒ a = 1/4 or a = 4

Hence, ‘4 and 1/4’ is the correct answer.