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Question 480147: the denominator of a fraction is an integer that is 3 more than the square of the numerator. if the fraction is reduced to lowest terms it equals 1/4. find the numerator.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! denominator of fraction is equal to 3 more than the square of the numerator.
n = the numerator
d = the denominator
our equation would be:
d = n^2 + 3
if the fraction is reduced to lowest terms, then it equals 1/4.
we have:
n/d = 1/4
since d = n^2 + 3, then we have:
n/(n^2 + 3) = 1/4
cross multiply to get:
4n = n^2 + 3
subtract 4n from both sides of the equation to get:
0 = n^2 - 4n + 3 which is the same as:
n^2 - 4n + 3 = 0
factor to get:
(n-3)*(n-1) = 0
this makes:
n = 3 or n = 1
if n = 1, then n/d = n/(n^2 + 3) which becomes 1/4.
if n = 3, then n/d = n/(n^2 + 3) which becomes 3/12.
since n = 1 results in the reduced fraction, it looks like the answer would be:
n = 3
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