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
The Absolute Best Book to challenge your Smart Student!
Original price was: $16.99.$11.99Current price is: $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
Original price was: $29.99.$14.99Current price is: $14.99.
Original price was: $29.99.$14.99Current price is: $14.99.
Satisfied 1 Students
Original price was: $24.99.$14.99Current price is: $14.99.
Satisfied 92 Students
Original price was: $24.99.$15.99Current price is: $15.99.
Satisfied 125 Students
Related to This Article
More math articles
- What Kind of Math Is on the ATI TEAS 7 Test?
- Top 10 Tips to Overcome TABE Math Anxiety
- How to Solve Powers of Products and Quotients? (+FREE Worksheet!)
- HSPT Math FREE Sample Practice Questions
- Top 10 Tips to ACE the ISEE Math Test
- How to Prepare for the CBEST Math Test?
- Top 10 Tips You MUST Know to Retake the ISEE Math
- How to Find Integers Equivalent Quotients
- Let’s Do the Math on Tesla’s Electric Cars
- Top 10 Tips to Overcome ISEE Math Anxiety
What people say about "Algebra Puzzle – Challenge 54 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.