SOLUTION: the sum of 2 consecutive reciprocals of 2 consecutive even integers is 9/40. what are the integers?

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Question 452008: the sum of 2 consecutive reciprocals of 2 consecutive even integers is 9/40. what are the integers?
Answer by stanbon(75887) About Me  (Show Source):
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the sum of 2 consecutive reciprocals of 2 consecutive even integers is 9/40. what are the integers?
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Integers:
1st: 2x
2nd: 2x+2
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Reciprocals:
1st: 1/(2x)
2nd: 1/(2x+2)
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Equation:
1/(2x) + 1/(2x+2) = 9/40
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Multiply thru by 40x(x+1) to get:
20(x+1) + 20x = 9x(x+1)
40x+20 = 9x^2+9x
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9x^2-31x-20 = 0
Positive solution: x = 4
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1st: 2x = 8
2nd: 2x+2 = 10
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Cheers,
Stan H.
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