Q. 144.0( 5 Votes )

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

Answer :

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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