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Question 821763: If the product of two positive numbers is 8 and their sum is 6, find the sum of their reciprocals
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! let n = first number
m = second number
(n)(m) = 8
n + m = 6
Solve for n in the equation n + m = 6
n + m = 6
subtract m from each side.
n = 6 - m
substitute ( 6 - m ) in (n)(m) = 8
( 6 - m )(m) = 8
distribute
6m - m^2 = 8
subtract 8 from each side and reorder
-m^2 + 6m - 8 = 0
multiply by -1
m^2 - 6m + 8 = 0
factor
(m - 2)(m - 4) = 0
So m = 2 or m = 4
Since n = 6 - m
for m = 2 , n = 4
for m = 4 , n = 2
So one way or the other we end up with the two numbers 2 and 4.
The sum of their reciprocals is 1/2 + 1/4 = 3/4
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