Asked by Anonymous
Two positive numbers differ by 2. Their reciprocals add to 3. Find the numbers. (keep your answer in simplest radical form)
Answers
Answered by
Damon
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
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
Answered by
Damon
LOL - Yes, the reciprocals actually do add to 3
Answered by
adds
what are the two answers then
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