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