Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 4"
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==Problem== | ==Problem== | ||
Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math> be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all positive integers <math>n</math>, | Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math> be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all positive integers <math>n</math>, | ||
| − | + | ||
| − | x_{n+1}+y_{n+1} | + | <cmath>x_{n+1}+y_{n+1} = 2x_n + 2y_n,</cmath> |
| − | x_{n+1}-y_{n+1} | + | <cmath>x_{n+1}-y_{n+1}=3x_n-3y_n.</cmath> |
| − | + | Find <math>x_5</math>. | |
==Solution== | ==Solution== | ||
asdf | asdf | ||
Revision as of 15:01, 11 July 2021
Problem
Let 
and 
be sequences of real numbers such that 
, 
, and, for all positive integers 
,
![\[x_{n+1}+y_{n+1} = 2x_n + 2y_n,\]](http://latex.artofproblemsolving.com/1/c/4/1c42c2eb43eee732142d0ce00d94594d1edf91fc.png)
![\[x_{n+1}-y_{n+1}=3x_n-3y_n.\]](http://latex.artofproblemsolving.com/2/2/7/227ff03360339f8aa8686718bc09680493a3c3d6.png)
Find 
.
Solution
asdf
