# 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 14:01, 11 July 2021

## Problem

Let and be sequences of real numbers such that , , and, for all positive integers ,

Find .

## Solution

asdf