If x is an integer…
We need to determine whether 9^x + 9^-x = b.
Statement One Alone:
3^x + 3^-x = √(b+2)
We first square both sides of the equation in statement one, obtaining:
(3^x + 3^-x)^2 = [√(b+2)]^2
(3^x + 3^-x)(3^x + 3^-x) = b+2
(3^x)(3^x) + (3^x)(3^-x) + (3^-x)(3^x) + (3^-x)(3^-x) = b + 2
3^(2x) + 3^0 + 3^0 + 3^(-2x) = b + 2
9^x + 1 + 1 + 9^-x = b + 2
9^x + 9^-x = b
Statement one is sufficient to answer to the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
Only knowing that x is greater than zero is not enough information to answer the question.