SOLUTION: please help me answer the following problem: find two consecutive positive even integers the difference of whose reciprocals is 1/60. thanks javier

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Question 24844: please help me answer the following problem:
find two consecutive positive even integers the difference of whose reciprocals is 1/60.
thanks
javier
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Try this Javier: Let n be the first positive even integer and n+2 be the next consecutive positive even integer. You can write the problem as:
1%2Fn+-+1%2F%28n%2B2%29+=+1%2F60 Add the fractions on the left. The common denominator is n%28n%2B2%29+=+n%5E2%2B2n
%28%28n%2B2%29+-+n%29%2F%28n%5E2%2B2n%29+=+1%2F60 Simplify and solve for n.
2%2F%28n%5E2%2B2n%29+=+1%2F60 Multiply both sides of the equation by 60.
120%2F%28n%5E2%2B2n%29+=+1 Multiply both sides by %28n%5E2%2B2n%29
120+=+n%5E2+%2B+2n Subtract 120 from both sides.
n%5E2+%2B+2n+-+120+=+0 Solve for n by factoring.
%28n+-+10%29%28n+%2B+12%29+=+0 Apply the zero products principle.
n+-+10+=+0 and/or n+%2B+12+=+0
If n+-+10+=+0 then n+=+10 This is the first positive even integer.
If n+%2B+12+=+0 the n+=+-12 Discard this solution as it is a negative integer.
The two integere are:
n = 10 and n+2 = 12
10 and 12
Check:
1%2F10+-+1%2F12+=+6%2F60+-+5%2F60 = %286-5%29%2F60+=+1%2F60