Alegebra 2

Two positive numbers differ by 2. Their reciprocals add to 3. Find the numbers. (keep your answer in simplest radical form)

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  1. n and n+2

    1/n + 1/(n+2) = 3
    (n+2) + n = 3 n(n+2) = 3 n^2 + 6 n
    2 n + 2 = 3 n^2 + 6 n

    3 n^2 + 4 n - 2 = 0

    n = [ -4 +/- sqrt (16 + 24) ]/6

    n = [ -4 +/- 2 sqrt (10) ]/6

    n = -2/3 +/- (1/3) sqrt 10

    says positive so use + sign

    (sqrt 10 -2)/3
    and
    (sqrt 10 -2)/3 + 6/3 = (4+sqrt 10)/3

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  2. LOL - Yes, the reciprocals actually do add to 3

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  3. what are the two answers then

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