Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

solve in R

solve in R

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: solve in R

I've managed to get two solutions for this... although I'm not sure if there are any more.

Dividing through by

(note that x = 0 is not a solution) gives :

Which can be rewritten as:

Making the substitution

gives:

Then making the substitution

gives:

From here,

is obviously a solution, which gives

The expression in terms of beta factorises to give:

I then thought I could say

, treat it as finding the sum of a geometric series to find the value of beta... but I ended up getting back to my original expression in terms of beta.

EDIT: Looking at it,

is obviously the only solution.... 9 1's are 9! And if beta is bigger than 1 the sum will clearly be bigger than 9... and if it's smaller than 1 then the sum will clearly be smaller than 9. So I *think* the two solutions I stated above are the only ones. (I'm sure that big expression factorises into something rather lovely, but there is no need to try to find it )

Last edited by Daniel123 (2008-08-08 19:18:33)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: solve in R

nice daniel

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solve in R

Very impressive work!

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It wanted to be normal.

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: solve in R

SUPERB!!

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve in R

AMAZING!