# 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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$11.99 Satisfied 123 Students 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 The Best Books to Ace Algebra$14.99
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