PSAT Math Multiple-Choice Question 686: Answer and Explanation

Question: 686

How many solutions does the following equation have?

• A. 0
• B. 1
• C. 2
• D. 4

Correct Answer: B

Explanation:

(B) Add to both sides while subtracting 6 from both sides:

If we square both sides, we can get rid of the square root:

a² - 12a + 36 = a

Subtract a from both sides to set the expression equal to 0:

a² - 13a + 36 = 0

Factoring tells us:

(a - 9)(a - 4) = 0

So a should equal 9 or 4. However, we have to be careful when square roots are involved. Although squaring both sides was useful when solving for a, this method can produce extraneous solutions. So we have to go back and check our answers to make sure that they are actually solutions to our original equation. Plug both numbers back in to the original equation to make sure that they work:

9 - 3 = 6

So 9 does work and is a solution to the original equation.

4 - 2 ≠ 6

So 4 is an extraneous solution. Therefore, there is only one solution, choice (B).