SE-SKOLORNAS 1974 Problem 5

Find the smallest positive real $t$ such that $$\left\{ \begin{array}{l} x_1 + x_3 = 2t x_2 x_2 + x_4 = 2t x_3 x_3 + x_5=2t x_4 \end{array} \right.$$ has a solution $x_1$ , $x_2$ , $x_3$ , $x_4$ , $x_5$ in non-negative reals, not all zero.