Algebra Puzzle – Challenge 54

This is a great math challenge for those who enjoy solving math and algebra challenges! The solution is also given.

Algebra Puzzle – Challenge 54

Challenge:

If \(9a^2 – b^2 = 11\) and a and b are positive integers, what is the value of \(a – b\)?

A- \(-5\)

B- \(-3\)

C- 3

D- 5

E- 7

The Absolute Best Book to challenge your Smart Student!

The correct answer is B.

Factorize \(9a^2 – b^2\) and 11
(3a – b) (3a + b) = 11 × 1
Therefore, 3a – b equals to 11 or 1 and 3a + b equals to 1 or 11.
Let’s check both:
3a – b = 1 and 3a + b = 11
Solve the above system of equation:
a = 2 and b = 5
3a – b = 11 and 3a + b = 1
a = 2 and b = – 5
Since, a and b are positive integers, then, only a = 2 and b = 5 are the solutions.
Therefore, a – b = 2 – 5 = -3

Related to "Algebra Puzzle – Challenge 54"

5 Essential Strategies in Teaching Math5 Essential Strategies in Teaching Math
Best Middle School Math SuppliesBest Middle School Math Supplies
10 Must-Have Elementary Classroom Math Supplies10 Must-Have Elementary Classroom Math Supplies
The Best School Supplies for Learning MathThe Best School Supplies for Learning Math
10 Must-Have Math Teacher Supplies10 Must-Have Math Teacher Supplies
Other Topics Puzzle – Challenge 100Other Topics Puzzle – Challenge 100
Other Topics Puzzle – Challenge 99Other Topics Puzzle – Challenge 99
Other Topics Puzzle – Challenge 98Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 97Other Topics Puzzle – Challenge 97
Other Topics Puzzle – Challenge 96Other Topics Puzzle – Challenge 96

What people say about "Algebra Puzzle - Challenge 54"?

No one replied yet.

Leave a Reply