I want inequality questons (1 Viewer)

[Constip8edSkunk]

there was 1 in my trials

 

[freaking_out]

Originally posted by turtle_2468
...Hmm. If I don't come up with any more, as I'm quite busy next few days, send me a PM around thursday and I'll think of a few...

yep, u can count on us to remind u.

 

[freaking_out]

Originally posted by ND
Are you referring to the projectile and line type q.? There is one of those in a 3u past paper.

yeah, me too i saw it in a 3u text....i think it was in the 3u 50 tips book.

 

[ND]

There was a proof of AM >= GM by induction in q8 '98. First two parts of the question were easy marks though.

 

[freaking_out]

Originally posted by ND
There was a proof of AM >= GM by induction in q8 '98. First two parts of the question were easy marks though.

is this proof in the arnold book?

 

[turtle_2468]

yeah, that one. I don't remember it as being too hard, but it's really messy...

 

[ND]

Originally posted by freaking_out
is this proof in the arnold book?

Well i'm looking at the harder 3u induction part of arnold, and i can't see it.

 

[freaking_out]

Originally posted by ND
Well i'm looking at the harder 3u induction part of arnold, and i can't see it.

so which book??

 

[ND]

Oh you thought i meant page 98? I meant the year '98. (i.e. it was from the 1998 HSC 4u paper)

 

[freaking_out]

Originally posted by ND
Oh you thought i meant page 98? I meant the year '98. (i.e. it was from the 1998 HSC 4u paper)

yeah, but if that concept is in the hsc, shouldn't it b in da textbook?

 

[ND]

Nope, you will find little (if any) of the q8 stuff in textbooks.

 

[freaking_out]

Originally posted by ND
Nope, you will find little (if any) of the q8 stuff in textbooks.

hmm...so i betta look at the past paper books.

 

[ND]

Also have a look at Bill Pender's harder 3u thing on drbuchanan's site. (afterall, q8 is almost always harder 3u)

 

[freaking_out]

Originally posted by ND
Also have a look at Bill Pender's harder 3u thing on drbuchanan's site. (afterall, q8 is almost always harder 3u)

oh yeah, forgot about that...i though it was in kinimini's site...nevermind

 

[ND]

Kinimini might have it on his site too (considering Pender was his teacher), but i got it from drbuchanan's.

 

[Richard Lee]

Originally posted by enak
For the AM-GM inequality, can't we just assume that? Or am I thinking about the Cauchy inequality (a1+a2+a3+...+an)/n >=nroot(a1a2a3...an) ?

Are you serious we have to prove that in the exam?

Yes!

If you check the past pater: Year 1998, you will find this questions!

But, I don't think you will find it in this year!

Good luck!

 

[Affinity]

there's a better proof in teh arnold book, page 242 example 8

 

[ND]

Wow, that's nice. I hadn't seen that before.

 

[Toodulu]

Originally posted by Richard Lee
The solution:
(a/b+b/c+c/d+d/a)/4>=4th sqrt[(a/b)(b/c)(c/d)(d/a)]=4
Same as:
(a1+a2+...+an)/n>=nth sqrt(a1*a2*...*an)

can we assume the 2nd bit if it hasn't been asked in the previous parts of the question?

 

[turtle_2468]

probably not. Usually questions like that lead up to it with
i) prove that a+b>=2*root(ab)
ii) prove that thing.
In which case you're supposed to use i) to prove it, and it's a bit of a copout really to just assume the AM-GM, seeing that you actually prove AM-GM by i)..