Question

The sum of a number and its reciprocal is `2 1/30`. Find the number. 

Answer 1

Let the required number be x.

According to the given condition, 

`x + 1/x = 2 1/30` 

⇒ `(x^2 + 1)/x = 61/30` 

⇒ 30x² + 30 = 61x 

⇒ 30x² – 61x + 30 = 0 

⇒ 30x² – 36x – 25x + 30 = 0 

⇒ 6x(5x – 6) – 5(5x – 6) = 0 

⇒ (5x – 6) (6x – 5) = 0 

⇒ 5x – 6 = 0 or 6x – 5 = 0

⇒ `x = 6/5` or `x = 5/6` 

Hence, the required number is `5/6` or `6/5`.