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

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
RELATED QUESTIONS
If the product of two positive numbers is 8 and their sum is 6, find the sum of their... (answered by jhunjiro)

if the sum of two numbers is 10 and their product is 5 what is the sum of their... (answered by josgarithmetic)

Two positive numbers differ by 4. If the sum of their reciprocals is 2/3, find these two... (answered by ben720)

The product of two numbers is 5 and the sum of their reciprocals is 9/10. Find the... (answered by checkley75)

The difference between two numbers is 8 and twice the sum of their reciprocals are equal... (answered by amarjeeth123)

the difference of two numbers is the same as their product, and the sum of their... (answered by josgarithmetic)

The sum of two numbers is 20. The sum of their reciprocals is 4/15. Find the two numbers (answered by stanbon,solver91311)

The sum of two numbers is 8 also 15 times the sum of their reciprocals is 8. Find the... (answered by ReadingBoosters)

The difference of two numbers is 4 and the sum of their reciprocals is 3/8. Find the... (answered by shree840)