The sum of a number and its reciprocal is 
. The number is
Let the required number be x
According to the question
20x2 - 41x + 20 = 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 = 20 b = - 41 c = 20
= 20.20 = 400
And either of their sum or difference = b
= - 41
Thus the two terms are - 25 and - 16
Difference = - 25 - 16 = - 41
Product = - 25. - 16 = 400
20x2 - 25x - 16x + 20 = 0
5x(4x - 5) - 4(4x - 5) = 0
(5x - 4) (4x - 5) = 0
28