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IMO 1995 — Official contest problems Question 4

IMO · IMO 1995 — Official contest problems

Question 4

The positive real numbers $x_0,x_1,\ldots,x_{1995}$ satisfy $x_0=x_{1995}$ and
$$x_{i-1}+\frac2{x_{i-1}}=2x_i+\frac1{x_i}$$
for $i=1,2,\ldots,1995$. Find the maximum value that $x_0$ can have.