IMO 1972 Problem 4

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*}