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
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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