Neka su
![x_1](/media/m/9/2/a/92aefd356eeab9982f45f21fb206a2ef.png)
,
![x_2](/media/m/a/a/1/aa16f4edacb7b534405242617406658f.png)
, ...,
![x_{100}](/media/m/c/c/2/cc28c9005485e35255e59b5ec2450d8e.png)
realni brojevi za koje vrijedi
![\begin{align*}
| 2x_k - x_{k+1} | &= x_{k+2} \quad \text{za sve } k\in \{1,2,\dotsc, 98\}, \\
| 2x_{99} - x_{100} | &= x_1, \\
| 2x_{100} - x_1 | &= x_2\text{.}
\end{align*}](/media/m/4/f/d/4fd1c033d6702f2fe59850c4c69e5a0e.png)
Dokaži da je
![x_1 = x_2 = \dotsb = x_{100}](/media/m/f/4/5/f4513d8f8eb273d4d63ccf5d11d226cf.png)
.
%V0
Neka su $x_1$, $x_2$, ..., $x_{100}$ realni brojevi za koje vrijedi $$$
\begin{align*}
| 2x_k - x_{k+1} | &= x_{k+2} \quad \text{za sve } k\in \{1,2,\dotsc, 98\}, \\
| 2x_{99} - x_{100} | &= x_1, \\
| 2x_{100} - x_1 | &= x_2\text{.}
\end{align*}
$$$ Dokaži da je $x_1 = x_2 = \dotsb = x_{100}$.