Question 20
(ROM 3) Solve the system of equations
$$\begin{aligned}x_1|x_1|&=x_2|x_2|+(x_1-a)|x_1-a|,\\x_2|x_2|&=x_3|x_3|+(x_2-a)|x_2-a|,\\&\cdots\\x_n|x_n|&=x_1|x_1|+(x_n-a)|x_n-a|,\end{aligned}$$
in the set of real numbers, where $a>0$.
$$\begin{aligned}x_1|x_1|&=x_2|x_2|+(x_1-a)|x_1-a|,\\x_2|x_2|&=x_3|x_3|+(x_2-a)|x_2-a|,\\&\cdots\\x_n|x_n|&=x_1|x_1|+(x_n-a)|x_n-a|,\end{aligned}$$
in the set of real numbers, where $a>0$.