# Algebra Puzzle – Challenge 54

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

## 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

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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

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