<PRE><B>Question 256684</B>
The sum of the reciprocals of 2 consecutive even integers is 11/60. Find the integers.
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Let the integers be:
1st 2x
2nd 2x+2
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Equation:
1/(2x) + 1/(2x+2) = 11/60
Multiply thru by 2 to get:
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1/x + 1/(x+1) = 11/30
(x+1 + x)/(x(x+1)) = 11/30
(2x+1)/(x^2+x) = 11/30
Cross-multiply
60x + 30 = 11x^2 + 11x
11x^2 - 49x - 30 = 0
(x-5)(11x+6) = 0
Positive solution:
x = 5
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1st number: 2x = 10
2nd number: 2x+2 = 12
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Cheers,
Stan H.
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