Difficult equation without unknown numbers

Algebra

Difficult equation without unknown numbers

Postby Guest » Sat May 02, 2020 1:45 am

The following Tn formulas calculate the n-th term of the Tribonacci sequence. The (2) is unknown and uses only one cubic root, since we can write [tex]b = (p + (4/p) + 1)/3[/tex], but how it is proved that (1) = (2)?

[tex]p = \sqrt [3] {19 + 3 \sqrt {33}}, p' = \sqrt [3] {19 - 3 \sqrt {33}}[/tex]

[tex]q = \sqrt [3] {586 + 102 \sqrt {33}}, q' = \sqrt [3] {586 - 102 \sqrt {33}}[/tex]

[tex]pp' = qq' = 4[/tex]

[tex]b = (p + p' + 1)/ 3, d = (q + q' + 1)/ 3[/tex]

[tex]T_n = [ b^{n - 1}/ (d - 1)] (1)[/tex]

[tex]T_n = [(b - 1)b^n/(4b - 6)] (2)[/tex]
Guest
 

Re: Difficult equation without unknown terms

Postby Guest » Sat May 02, 2020 2:06 am

Guest wrote:The following Tn formulas calculate the n-th term of the Tribonacci sequence. The (2) is unknown and uses only one cubic root, since we can write [tex]b = (p + (4/p) + 1)/3[/tex], but how it is proved that (1) = (2)?

[tex]p = \sqrt [3] {19 + 3 \sqrt {33}}, p' = \sqrt [3] {19 - 3 \sqrt {33}}[/tex]

[tex]q = \sqrt [3] {586 + 102 \sqrt {33}}, q' = \sqrt [3] {586 - 102 \sqrt {33}}[/tex]

[tex]pp' = qq' = 4[/tex]

[tex]b = (p + p' + 1)/ 3, d = (q + q' + 1)/ 3[/tex]

[tex]T_n = [ b^{n + 1}/ (d - 1)] (1)[/tex]

[tex]T_n = [(b - 1)b^n/(4b - 6)] (2)[/tex]
Guest
 


Return to Algebra



Who is online

Users browsing this forum: No registered users and 1 guest

cron