Difference between revisions of "1995 OIM Problems/Problem 2"
(Created page with "== Problem == Let <math>n</math> be an integer greater than 1. Determine the real numbers <cmath>X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X+{n+1} > 0</cmath> that verify t...") |
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== Problem == | == Problem == | ||
| − | Let <math>n</math> be an integer greater than 1. | + | Let <math>n</math> be an integer greater than 1. Find the real numbers |
<cmath>X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X+{n+1} > 0</cmath> | <cmath>X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X+{n+1} > 0</cmath> | ||
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a. <math>X_1^{1/2} + X_2^{3/2} + \cdots + X_n^{n+1/2} = n.X_{n+1}^{1/2}</math> | a. <math>X_1^{1/2} + X_2^{3/2} + \cdots + X_n^{n+1/2} = n.X_{n+1}^{1/2}</math> | ||
b. <math>(X_1 + X_2 + \cdots + X_n)/n = X_{n+1}</math> | b. <math>(X_1 + X_2 + \cdots + X_n)/n = X_{n+1}</math> | ||
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~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Revision as of 14:44, 13 December 2023
Problem
Let 
be an integer greater than 1. Find the real numbers
![\[X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X+{n+1} > 0\]](http://latex.artofproblemsolving.com/f/f/5/ff5049160119dc48f2886b7edbad5330241f5058.png)
that verify the following two conditions:
a. 
b. 
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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