IMO Shortlist 1972 problem 9
Dodao/la:
arhiva2. travnja 2012. Find all positive real solutions to:
%V0
Find all positive real solutions to: $$$\begin{eqnarray*}
(x_1^2-x_3x_5)(x_2^2-x_3x_5) &\le& 0 \\
(x_2^2-x_4x_1)(x_3^2-x_4x_1) &\le& 0 \\
(x_3^2-x_5x_2)(x_4^2-x_5x_2) &\le& 0 \\
(x_4^2-x_1x_3)(x_5^2-x_1x_3) &\le& 0 \\
(x_5^2-x_2x_4)(x_1^2-x_2x_4) &\le& 0
\end{eqnarray*}$$$
Izvor: Međunarodna matematička olimpijada, shortlist 1972
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