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

Answer 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

Answer 2

LOL - Yes, the reciprocals actually do add to 3

Answer 3

what are the two answers then