If A + B = 18, and A x B = 72, then A2 + B2 = ___________
You do not need to solve for the individual values of A and B to answer this problem, but you must show your work using ALGEBRA.
Solution to the Problem:
The answer is A2 + B2 = 180
(A + B)2 = A2 + 2 AB + B2
Since A + B = 18 and A x B = 72, Then 182 = A2 +2 (72) + B2
Then 324 = A2 + 144 + B2
So, A2 + B2 = 180
Of course, you can also solve 2 simultaneous equations to obtain A = 6 and B = 12 (or vice versa).
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Brijesh Dave | Mumbai City, Maharashtra, India |
| 3. Jacob Branson |
Mountain View High School, Mountain View, Wyoming |
| 4. Marivi Bungay-Domingo | Philippines |
| 5. Mairany Jaracuaro |
Delta High School, Delta, Colorado |
| 6. Gauge Lockhart |
Delta High School, Delta, Colorado |
| 7. Ivy Joseph | Pune, Maharashtra, India |
| 8. Faith Pfeifer |
Mountain View High School, Mountain View, Wyoming |
| 9. Hope Pfeifer |
Mountain View High School, Mountain View, Wyoming |