HSC 2015 MX2 Marathon ADVANCED (archive) (4 Viewers)

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

While you're here Dan, please clarify your weird functional equation question on the newer advanced marathon.

which one?

 

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

While you're here Dan, please clarify your weird functional equation question on the newer advanced marathon.

which one? I don't remember posing questions, only quoting what the current question was which was posted by simpleetal.

the only other reference was just me trying to wrap around some-one else question, so not actually a question posed.

 

[Paradoxica]

Re: HSC 2015 4U Marathon - Advanced Level

which one? I don't remember posing questions, only quoting what the current question was which was posted by simpleetal.

the only other reference was just me trying to wrap around some-one else question, so not actually a question posed.

 

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

can you link the original question, for context. cannot seem to find it.

 

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

can you link the original question, for context. cannot seem to find it.

corrected question for clarity.

 

[InteGrand]

Re: HSC 2015 4U Marathon - Advanced Level

corrected question for clarity.

For anyone interested, here is the edited version:

** If f(nx) and g(nx) are to such that in terms of a polynomial; whereby
the sum of the roots in any amount (individually, in pairs, triples etc.) or the product of the roots is the same value - an integer
==> the coefficients of the polynomial are identical and integer values.


And also that g(x) = sqrt(1 - f(x)^2)
Show that n=5 is the first integer solution, apart from any trivial cases.

This question requires a bit of intuition.
edit: identical is wrong word maybe.

 

[glittergal96]

Re: HSC 2015 4U Marathon - Advanced Level

This wording is not really any clearer imo.

 

[InteGrand]

Re: HSC 2015 4U Marathon - Advanced Level

This wording is not really any clearer imo.

Yeah. I just posted it here to save people trouble of having to search it. Haha

 

[Paradoxica]

Re: HSC 2015 4U Marathon - Advanced Level

This wording is not really any clearer imo.

The question, as I interpret it is...

Prove, that in the polynomial expansion of cos(nx) and sin(nx), they will only be identical if and only if n is odd (subject to trivial cases)

 

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

For anyone interested, here is the edited version:

Sorry, don't know what I was thinking last night. The edited version isn't any clearer, and still has the error that the original did which I noticed just then.

Really, it is actually a simple question, my poor wording made what should be a very simple question reducible to something very simple/almost trivial, as noted above; unable to be done...

(more suitable for normal 4u thread)

The function f(x) and g(x) are given so that for n>0

f(nx) is some H(f(x))
g(nx) is some G(g(x))

If f(x)^2+g(x)^2=1
demonstrate (using Demoivre's theorem without resorting to induction) that functions H(y) and G(y) are identical for when n=1, 5, 9...

 

[Paradoxica]

Re: HSC 2015 4U Marathon - Advanced Level

Sorry, don't know what I was thinking last night. The edited version isn't any clearer, and still has the error that the original did which I noticed just then.

Really, it is actually a simple question, my poor wording made what should be a very simple question reducible to something very simple/almost trivial, as noted above; unable to be done...

(more suitable for normal 4u thread)

The function f(x) and g(x) are given so that for n>0

f(nx) is some H(f(x))
g(nx) is some G(g(x))

If f(x)^2+g(x)^2=1
demonstrate (using Demoivre's theorem without resorting to induction) that functions H(y) and G(y) are identical for when n=1, 5, 9...

 

[dan964]

Re: HSC 2015 4U Marathon - Advanced Level

didn't do it in latex, otherwise yes would have put it like that.