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

Revision as of 02:31, 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.

Revision as of 02:30, 22 April 2020 (view source) Alapan1729 (talk \| contribs) ← Older edit		Revision as of 02:31, 22 April 2020 (view source) Alapan1729 (talk \| contribs) Newer edit →
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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	+	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>