Let x be a positive integer such that
$$\frac { 10 x } { x + 3 }$$
is equal to the square of an integer. What is the sum of the values that x can take?
A) 26
B) 27
C) 29
D) 31
E) 32

Let $(a_n)$ be a geometric sequence. The equality
$$\frac { a _ { 5 } - a _ { 1 } } { \left( a _ { 3 } \right) ^ { 2 } - \left( a _ { 1 } \right) ^ { 2 } } = \frac { 4 } { 9 }$$
is given. Given that $a _ { 2 } = \frac { 3 } { 2 }$, what is $a _ { 4 }$?
A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 27 } { 8 }$
E) $\frac { 27 } { 4 }$

For a geometric sequence $(a_n)$ with all positive terms and common ratio $r$
$$\begin{aligned} & a_1 + \frac{1}{2} + r \\ & a_7^2 = a_5 + 12 \cdot a_3 \end{aligned}$$
the equalities are given.