Q. 173.8( 8 Votes )

The sum of a natural number and its reciprocal is 65/8. Find the number.

Answer :

Let the required natural numbers x

According to given condition,






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 = 8 b = – 65 c = 8


= 8.8 = 64


And either of their sum or difference = b


= – 65


Thus the two terms are – 64 and – 1


Difference = – 64 – 1 = – 65


Product = – 64. – 1 = 64



8x (x – 8) – 1(x – 8) = 0


(x – 8) (8x – 1) = 0


(x – 8) = 0 or (8x – 1) = 0


x = 8 or x = 1/8


x = 8 (x is a natural number)


Hence the required number is 8.


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