October 2017
Problem of the Month

Another A and B problem

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

Send any comments or questions to: David Pleacher