A2. For some integer $x$, the finite sequence $\sqrt{x}+2, 3 \sqrt{x+1}, 2 \sqrt{x}+4$ is geometric. What is the common ratio of this sequence?
(A) 2
(B) $\sqrt{3}$
(C) $\sqrt{2}$
(D) 3
(E) $3 \sqrt{2}$
A2. We consider the relationship between consecutive terms of a geometric sequence. We solve the irrational equation and obtain the solutions $x_{1}=1$ and $x_{2}=\frac{1}{49}$. The only integer solution is 1. Then we calculate the terms of the sequence $a_{1}=3, a_{2}=3 \sqrt{2}, a_{3}=6$. We calculate the common ratio $q=\sqrt{2}$. The correct answer is C.