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HSC 2016 MX2 Marathon ADVANCED (archive) (2 Viewers)

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glittergal96

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Re: HSC 2016 4U Marathon - Advanced Level

For the polynomial question without assuming C-S:




Also, I wouldn't consider C-S an "elegant" solution to the inequality as posed to a high school student given that the inequality in this question in the first place is just a special case of C-S itself, and C-S is outside assumed knowledge.

That's kind of like citing AM-GM in n variables in a proof of AM-GM in 3 variables. Sure your proof will then be short, but it is only artificially short, as if you fleshed it out into a full path from MX2 assumed knowledge to the claimed statement, you are first walking past your target statement and then doubling back.
 

glittergal96

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Re: HSC 2016 4U Marathon - Advanced Level

From the definition of g, we have



So upon multiplying both sides of the equation



by , we are left with



The claim then follows by equating the coefficients of degree n-1 on both sides.
 

lita1000

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Re: HSC 2016 4U Marathon - Advanced Level

A difficult question which one of my students asked me the other day:

 

lita1000

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Re: HSC 2016 4U Marathon - Advanced Level

Let's see if one of the BOS members can crack it
 

KX

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Re: HSC 2016 4U Marathon - Advanced Level

Okay got sent here by a user called Integrand, can someone post a good question please?
 

InteGrand

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Re: HSC 2016 4U Marathon - Advanced Level

I'll requote the unsolved problems from the previous marathons.
I do remember some of these had solutions posted up (e.g. definitely remember simpleetal posting up his solution to his problem).
 

Paradoxica

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Re: HSC 2016 4U Marathon - Advanced Level

Yeah, I couldn't really wrap my mind around that. Someone needs to summon him and acquire a clarification of the question, or perhaps the corrected version.

Also, there's my circle geo problem up there, which is beyond the scope of the Ext. 2 course.
 

Librah

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Re: HSC 2016 4U Marathon - Advanced Level

Prove there can be no positive integers a,b,c for n>2 that can satisfy the equation a^n+b^n=c^n. Popular question in many past papers.
 

Paradoxica

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Re: HSC 2016 4U Marathon - Advanced Level

Prove there can be no positive integers a,b,c for n>2 that can satisfy the equation a^n+b^n=c^n. Popular question in many past papers.
.
Pierre de Fermat said:
Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.
 
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