Define a sequence of ordered pairs (x;, y;) as follows: (xo, Yo) = (3,1) %3D Xn+1 = 3xn + 4yn, n > 0 Yn+1 = 2xn + 3yn, n > 0 rove that for every n 2 0, (xn, Yn) satisfies the equation x2 – 2y2 = 7. %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 13E
Topic Video
Question
Define a sequence of ordered pairs (x;, yi) as follows:
(xo, Yo)
(3,1)
Хn+1
3xn + 4yn,
n > 0
Уп+1
2хn + Зуп,
n > 0
Prove that for every n 2 0, (xn, Yn) satisfies the equation x2 – 2y2 = 7.
Transcribed Image Text:Define a sequence of ordered pairs (x;, yi) as follows: (xo, Yo) (3,1) Хn+1 3xn + 4yn, n > 0 Уп+1 2хn + Зуп, n > 0 Prove that for every n 2 0, (xn, Yn) satisfies the equation x2 – 2y2 = 7.
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