SOLUTION: If the product of two positive numbers is 8 and their sum is 6, find the sum of their reciprocals

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Question 821765: If the product of two positive numbers is 8 and their sum is 6, find the sum of their reciprocals
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
x - 1st positive integer
y - 2nd positive integer
-
xy=8 eq 1
-
x%2By=6eq 2
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Solution:
-formulate eq 1
x=8%2Fyeq3
-then subtitute eq 3 to eq 2
%288%2Fy%29%2By=6
-multiply both sides by y
8%2By%5E2=6y
-
y%5E2-6y%2B8=0
-factor
%28y-2%29%28y-4%29=0
-
highlight%28y=2%29
-
reciprocalhighlight%28y=1%2F2%29
-
x=8%2F2
-
highlight+%28x=4%29
-
reciprocalhighlight+%28x=1%2F4%29
-
sum of their reciprocal
-
1%2F2%2B1%2F4%29 LCD=4
%282%2B1%29%2F4%29
=highlight+%283%2F4%29%29