SOLUTION: . The sum of the reciprocals of two consecutive positive odd integers is 16/63. Find the integers.

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Question 610037: . The sum of the reciprocals of two consecutive positive odd integers is 16/63. Find the integers.
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

The sum of the reciprocals of two consecutive positive odd integers is 16/63

1%2F%28n%29+%2B+1%2F%28n%2B2%29+=+16%2F63

  63(n+2) + 63n = 16n(n+2)              |||Multiplying thru by 63n(n+2) so as all denominators = 1

  16n^2 - 94n - 126 = 0

x+=+%2894+%2B-+sqrt%2816900+%29%29%2F%2832%29+

  n = 7, tossing out negative solution

   7 and 9 are the two consecutive positive odd integers

CHECKING our Answer***

1/7 + 1/9 = 16/63

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the reciprocals of two consecutive positive odd integers is 16/63. Find the integers.
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1st: 2x-1
2nd: 2x+1
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Equation:
1/(2x-1) + 1/(2x+1) = 16/63
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Multiply thru by 63*(2x-1)(2x+1) to get:
63(2x+1) + 63(2x-1) = 16(4x^2-1)
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126x + 63 + 126x - 63 = 64x^2 - 16
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64x^2 - 252x - 16 = 0
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Divide thru by 4 to get:
16x^2 - 63x - 4 = 0
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16x^2-64x+x-4 = 0
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16x(x-4)+(x-4) = 0
(x-4)(16x+1) = 0
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x = 4 or x = -1/16
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If x = 4
2x-1 = 7
2x+1 = 9
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cheers,
Stan H.
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