Question

If (p) and (n) are integers such that p>n>0 and p² - n² =12, which of the following can be the value of p - n?

1) 1
2) 2
3) 4

Answer 1

The possible value of p - n that satisfies the equation p² - n² = 12 is 4 when p = 6 and n = 2.

Step-by-step explanation:

The question asks for possible values of p - n given that (p) and (n) are integers, p > n > 0, and p² - n² = 12. To find the values of p - n, we can factor the given equation as (p + n)(p - n) = 12. Because p and n are integers, and p - n must also be an integer, we can determine the integer pairs that multiply to 12 and satisfy p > n. These pairs are (12, 1), (6, 2), and (4, 3). The p - n values corresponding to these pairs are 12 - 1 = 11, 6 - 2 = 4, and 4 - 3 = 1 respectively.

Out of the given options for p - n, the only value that can be formed from these pairs is 4. Therefore, the correct choice for the value of p - n is 4, as it can be achieved if p = 6 and n = 2.