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

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) (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

63(n+2) + 63n = 16n(n+2) |||Multiplying thru by 63n(n+2) so as all denominators = 1
16n^2 - 94n - 126 = 0

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) (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
=================
cheers,
Stan H.
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