fardeen2 fardeen2
  • 15-05-2016
  • Mathematics
contestada

Find 2 consecutive odd numbers given that difference between their resiprocal is 2/63

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Alphabette
Alphabette Alphabette
  • 15-05-2016
Those odd numbers are nine and seven.
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padawan
padawan padawan
  • 15-05-2016
consecutive odd numbers are 2n+1, 2n+3

difference of reciprocals
1/(2n+1) - 1/(2n+3) = 2/63
((2n+3) - (2n+3))/(2n+1)(2n+3) =2/63
2/(4n^2 + 8n +3) =2/63
4n^2 + 8n +3 = 63
4n^2 + 8n -60 = 0
n^2 + 2n - 15 = 0
(n + 5)(n - 3) = 0
n = 3 (only positive)
numbers are 2(3)+1=7 and 9
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