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

Let the required number be x.

According to the given condition,

30x^{2} + 30 = 61x

30x^{2} – 61x + 30 = 0

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 30 b = – 61 c = 30

= 30.30 = 900

And either of their sum or difference = b

= – 61

Thus the two terms are – 36 and – 25

Sum = – 36 – 25 = – 61

Product = – 36. – 25 = 900

30x^{2} – 36x – 25x + 30 = 0

6x(5x – 6) – 5(5x – 6) = 0

(5x – 6) (6x – 5) = 0

(5x – 6) = 0 or (6x – 5) = 0

Hence the required number is

28