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 |