The difference of two natural numbers is 3 and the difference of their 3 reciprocals is 3/28.Find the numbers.

Let the required natural numbers x and (x + 3)

x < x + 3

Thus

According to given condition,

taking LCM

cross multiplying

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 = 1 b = 3 c = – 28

= 1. – 28 = – 28

And either of their sum or difference = b

= 3

Thus the two terms are 7 and – 4

Difference = 7 – 4 = 3

Product = 7. – 4 = – 28

x(x + 7) – 4(x + 7) = 0

(x – 4) (x + 7) = 0

(x – 4) = 0 or (x + 7) = 0

x = 4 or x = – 7

x = 4 (x < x + 3)

x + 3 = 4 + 3 = 7

Hence required numbers are 4 and 7.

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