7. Let $x, y, z$ be real numbers, $3 x, 4 y, 5 z$ form a geometric sequence, and $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ form an arithmetic sequence, then the value of $\frac{x}{z}+\frac{z}{x}$ is $\qquad$ .
$$
\begin{array}{l}
\frac{2}{y}=\frac{1}{x}+\frac{1}{z} \Rightarrow y=\frac{2 x z}{x+z} \Rightarrow 16 y^{2}=\frac{64 x^{2} z^{2}}{(x+z)^{2}}=15 x z \Rightarrow 64 x z=15(x+z)^{2} \\
\Rightarrow 15\left(x^{2}+z^{2}\right)=34 x z \Rightarrow \frac{x}{z}+\frac{z}{x}=\frac{x^{2}+z^{2}}{x z}=\frac{34}{15} .
\end{array}
$$

The translation is as follows:

$$
\begin{array}{l}
\frac{2}{y}=\frac{1}{x}+\frac{1}{z} \Rightarrow y=\frac{2 x z}{x+z} \Rightarrow 16 y^{2}=\frac{64 x^{2} z^{2}}{(x+z)^{2}}=15 x z \Rightarrow 64 x z=15(x+z)^{2} \\
\Rightarrow 15\left(x^{2}+z^{2}\right)=34 x z \Rightarrow \frac{x}{z}+\frac{z}{x}=\frac{x^{2}+z^{2}}{x z}=\frac{34}{15} .
\end{array}
$$