Difference between revisions of "1995 OIM Problems/Problem 2"
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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}\; | + | <cmath>X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X_{n+1} > 0</cmath> |
that verify the following two conditions: | that verify the following two conditions: | ||
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 | ||
Latest revision as of 13:45, 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/5/3/0/530214224c75e061c9028e3220be41cd44cb3739.png)
that verify the following two conditions:
a. 
b. 
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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