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Question 373161: The difference of the reciprocals of two consecutive even integers is 1/12 Find the Integers
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! The difference of the reciprocals of two consecutive even integers is 1/12 Find the Integers
let n be one integer
let n + 2 be the next consecutive even integer
1/n - 1/(n + 2) = 1/12
12/n - 12/(n + 2) = 1
12 - 12n/(n + 2) = n
12(n + 2) - 12n = n(n + 2)
12n + 24 - 12n = n^2 + 2n
24 = n^2 + 2n
0 = n^2 + 2n - 24
0 = (n - 4)(n + 6) (by FOIL this same, 6n - 4n = 2n)
n = 4 or n = -6
check:
1/4 - 1/6 = 1/4 * 3/3 - 1/6 * 2/2 = 3/12 - 2/12 = 1/12, yes
1/(-6) - 1/(-4) = -1/6 + 1/4 = -1/6 * 2/2 + 1/4 * 3/3 = -2/12 + 3/12 = 1/12, yes
4 and 6 or -6 and -4 are answers
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