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Find the number of solutions, in positive real numbers, to the system
\(\begin{align*} x_1 + \frac{1}{x_2} &= 4, \\ x_2 + \frac{1}{x_3} &= 1, \\ x_3 + \frac{1}{x_4} &= 4, \\ x_4 + \frac{1}{x_5} &= 1, \\ &\dots, \\ x_{99} + \frac{1}{x_{100}} &= 4, \\ x_{100} + \frac{1}{x_1} &= 1. \end{align*}\)

 Aug 8, 2021
 #1
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Adding up all the equations and using an AM-GM estimate, we get that the system has no solutions.

 Aug 8, 2021
 #2
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Its not right

Guest Aug 9, 2021
 #3
avatar+32561 
+1

Spot the pattern:

 

... etc.

 Aug 10, 2021
 #4
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thanks!

Guest Aug 11, 2021

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