SOLUTION: if the sum of the two numbers is 15 and the product of the two numbers is 5, find the sum of the reciprocal a of the two numbers. show your work.

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Question 1004438: if the sum of the two numbers is 15 and the product of the two numbers is 5, find the sum of the reciprocal a of the two numbers. show your work.
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=15%2Cxy=5%29 and you are interested in finding 1%2Fx%2B1%2Fy.

To begin, x%2815-x%29=5
15x-x%5E2=5
x%5E2-15x%2B5=0

x=%2815%2B-+sqrt%2815%5E2-4%2A5%29%29%2F2

x=%2815%2B-+sqrt%28225-20%29%29%2F2

x=%2815%2B-+sqrt%28205%29%29%2F2

The two numbers are %2815-sqrt%28205%29%29%2F2 and %2815%2Bsqrt%28205%29%29%2F2.
A little more arithmetic to find the answer to the question.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If the sum of the two numbers is 15, and the product of the two numbers is 5, find the sum of the reciprocal a of the two numbers.
:
find a & b
a + b = 15
b = (-a + 15)
and
a*b = 5
replace b with (-a+15)
a(-a+15) = 5
-a^2 + 15a - 5 = 0
multiply by -1 and solve completing the square
a^2 - 15a + ___ = -5
a^2 - 15a + 56.25 = -5 + 56.25
a^2 - 15a + 56.25 = 51.25
(a - 7.5)^2 = 51.25
a - 7.5 = +/-sqrt%2851.25%29
Two solutions
a = 7.5 + sqrt%2851.25%29 then b = 7.5- sqrt%2851.25%29
and
a = 7.5 - sqrt%2851.25%29 then b = 7.5 + sqrt%2851.25%29
The sum of the reciprocal using a calc
1%2F%287.5%2Bsqrt%2851.25%29%29 + 1%2F%287.5-sqrt%2851.25%29%29 = 3