Question

Which of the following statements are equivalent to "there exists at least one integer n such that n^2 = 25"?

a. n=5 or n=−5
b. n=4 or n=−4
c. n=3 or n=−3
d. n=2 or n=−2

Answer 1

The statement implies finding integer solutions for n^2 = 25, which are n=5 or n=-5. Thus, the correct answer is a. n=5 or n=-5.

Step-by-step explanation:

The statement "there exists at least one integer n such that n^2 = 25" implies that we are looking for integer solutions to the equation n^2 = 25. When we solve this equation, we find that n can be either 5 or -5, because both 5^2 and (-5)^2 equal to 25. Therefore, the correct answer to this question is a. n=5 or n=−5, since these are the two integers that satisfy the given equation.