3.15. Find all positive solutions ($x_{1}>0, x_{2}>0$, $x_{3}>0, x_{4}>0, x_{5}>0$) of the system of equations

$$
\left\{\begin{array}{l}
x_{1}+x_{2}=x_{3}^{2} \\
x_{2}+x_{3}=x_{4}^{2} \\
x_{3}+x_{4}=x_{5}^{2} \\
x_{4}+x_{5}=x_{1}^{2} \\
x_{5}+x_{1}=x_{2}^{2}
\end{array}\right.
$$

## 3.4. The number of solutions of the system of equations
3.15. Let $x_{\min }=x_{i}$ be the smallest of the numbers $x_{1}, \ldots, x_{5}, x_{\max }=$ $=x_{j}$ be the largest. Then $x_{\min }^{2}=x_{i-2}+x_{i-1} \geqslant 2 x_{\min }$ (here it is assumed that $x_{0}=x_{5}$ and $x_{-1}=x_{4}$) and $x_{\max }^{2}=x_{j-2}+x_{j-1} \leqslant 2 x_{\max }$.

The numbers $x_{\min }$ and $x_{\max }$ are positive, so $x_{\min } \geqslant 2 \geqslant x_{\max }$. Therefore, $x_{\min }=x_{\max }=2$.