Q. 28

# The sum of a number and its reciprocal is . The number isA. B. C. D.

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

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