the sum of reciporacal of 2 consecutive natural numbers is 23/132 . find the numbers

Asked by Kamal Preet | 14th Nov, 2013, 06:34: PM

Expert Answer:

Let the two consecutive natural numbers be x and x + 1.
Then, their reciprocals will be 1/x and 1/x+1
Thus, 
264x + 132 = 23x2 + 23x
23x2 - 241x - 132 = 0
23x2 - 253x + 12x - 132 = 0

23x(x - 11) + 12(x - 11)

Thus, x = 11 and x = -12/23

But as it is a natural number, -12/23 is not valid.

Thus, x = 11

Hence, two consecutive natural numbers are 11 and 11 + 1 = 12.

Answered by Rashmi Khot | 15th Nov, 2013, 06:07: PM

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