December 2018
Problem of the Month

Sum and Product

The sum of two numbers is 2.

The product of these same two numbers is 5.

Determine the sum of their reciprocals.

You must show your algebra in order to get credit for this problem.

Solution to the Problem:

The sum of the reciprocals is 2/5.

There are two ways to approach this problem.

(1) Set up equations and solve for the numbers.   Then add their reciprocals together.

x + y = 2
x y = 5

Then y = 5/x
So, x + 5/x = 2
Then x^2 + 5 = 2x
so x = 1 ± 2i
and y = 1 ∓ 2i

Adding the reciprocals, 1/(1+2i) + 1/(1-2i) = (1 + 2i + 1 - 2i) / (1 + 4) = 2/5

(2) Solve for the reciprocals immediately.

1/x + 1/y = (x + y) / xy = 2/5

Correctly solved by:

1. Ivy Joseph	Pune, Maharashtra, India
2. Kayla Teel	Delta High School, Delta, Colorado
3. Sameha Haque	Delta High School, Delta, Colorado
4. Caleb Frazier	Delta High School, Delta, Colorado
5. James Alarie	Flint, Michigan
6. Brisa Rodriguez	Delta High School, Delta, Colorado
7. Makayla Kortz	Delta High School, Delta, Colorado
8. Morgan Redden	Delta High School, Delta, Colorado
9. Olivia Santonastaso	Delta High School, Delta, Colorado
10. Alexander Thomas	Mountain View High School, Mountain View, Wyoming
11. Tyler Stoddard	Mountain View High School, Mountain View, Wyoming
12. Kenzy Kellum	Mountain View High School, Mountain View, Wyoming
13. Charity Harmon	Mountain View High School, Mountain View, Wyoming
14. Cortlin Condos	Mountain View High School, Mountain View, Wyoming
15. Somer Cannon	Delta High School, Delta, Colorado
16. Jaynee Hunt	Mountain View High School, Mountain View, Wyoming
17. Aubree Andre	Delta High School, Delta, Colorado
18. Dawson Jorgensen	Mountain View High School, Mountain View, Wyoming
19. Kamri Hutchings	Mountain View High School, Mountain View, Wyoming
20. Michael Newton	Mountain View High School, Mountain View, Wyoming
21. Kaycee Bugas	Mountain View High School, Mountain View, Wyoming
22. Dalia Fleischhauer	Mountain View High School, Mountain View, Wyoming
23. Bridger Harris	Mountain View High School, Mountain View, Wyoming
24. Reagan Clay	Delta High School, Delta, Colorado
25. Elena Melgoza	Delta High School, Delta, Colorado
26. Shania Ballard	Delta High School, Delta, Colorado
27. Eli Farmer	Delta High School, Delta, Colorado
28. Brijesh Dave	Mumbai City, Maharashtra, India
29. Rob Miles	Northbrook, Illinois

Send any comments or questions to: David Pleacher