Difference between revisions of "1995 IMO Problems/Problem 4"

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The positive real numbers <math>x_0, x_1, x_2, x_3, x_4.....x_{1994}, x_{1995}</math> satisfy the relations  
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The positive real numbers <math>x_0, x_1, x_2,.....x_{1994}, x_{1995}</math> satisfy the relations  
  
 
<math>x_0=x_{1995}</math> and <math>x_{i-1}+\frac{2}{x_{i-1}}=2{x_i}+\frac{1}{x_i}</math>  
 
<math>x_0=x_{1995}</math> and <math>x_{i-1}+\frac{2}{x_{i-1}}=2{x_i}+\frac{1}{x_i}</math>  

Revision as of 03:31, 22 April 2020

The positive real numbers $x_0, x_1, x_2,.....x_{1994}, x_{1995}$ satisfy the relations

$x_0=x_{1995}$ and $x_{i-1}+\frac{2}{x_{i-1}}=2{x_i}+\frac{1}{x_i}$

for $i=1,2,3,....1995$

Find the maximum value that $x_0$ can have.