CBSE Class 10 Answered
the sum of reciporacal of 2 consecutive natural numbers is 23/132 . find the numbers
Asked by Kamal Preet | 14 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 | 15 Nov, 2013, 06:07: PM
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