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x_1 + x_3 = 2t x_2 , x_2 + x_4 = 2t x_3 , x_3 + x_5=2t x_4

Source: 1974 Swedish Mathematical Competition p5

March 26, 2021
system of equationsSystemalgebra

Problem Statement

Find the smallest positive real tt such that {x1+x3=2tx2x2+x4=2tx3x3+x5=2tx4\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 x1x_1, x2x_2, x3x_3, x4x_4, x5x_5 in non-negative reals, not all zero.
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