Q. 124.3( 9 Votes )

The sum of two natural numbers is 9 and the sum of their reciprocals is 1/2. Find the numbers.

Answer :

Let the required natural numbers x and (9 – x)

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 = – 9 c = 18


= 1.18 = 18


And either of their sum or difference = b


= – 9


Thus the two terms are – 6 and – 3


Sum = – 6 – 3 = – 9


Product = – 6. – 3 = 18




x(x – 6) – 3(x – 6) = 0


(x – 6) (x – 3) = 0


(x – 6) = 0 or (x – 3) = 0


x = 6 or x = 3


Case I: when x = 6


9 – x = 9 – 6 = 3


Case II: when x = 3


9 – x = 9 – 3 = 6


Hence required numbers are 3 and 6.


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