hard inequalities question (1 Viewer)

[member 6003]

I found this question in the JRHS 2023 paper that was upload here recently. I skipped it when I did the practise test, but when I went over it again I still couldn't get it. I asked my teacher and she hasn't gotten it as of yet. Could anyone help with this?

stuff you probably have to use:



I tried subbing in a-> (a^3+1)^(1/3) etc but didn't result in anything useful
i did some other manipulation and got this but I don't think it's useful either:


seems like using expanding LHS doesn't get anywhere useful since there is no way to get to the RHS.

 

[synthesisFR]

wait where is the paper

 

[member 6003]

wait where is the paper

notes and resources

 

[its_ace21]

wait where is the paper

isnt it the one where u said it ruined ur life

 

[synthesisFR]

oh James UwUse

 

[member 6003]

View attachment 39660

you go to ruse right? did anyone actually get this in the test?

 

[carrotsss]

View attachment 39660

I just spent ages getting this with a ton of algebra bashing and like 50 individual inequalities (which somehow worked) was it really this easy all along

 

[carrotsss]

yeah but just be glad you didn't get marked down for your 2 looking like a 3

I probably would’ve been, the quality of my 2s really degraded after the first page

 

[member 6003]

i'm pretty sure most/all of top 5 would've gotten it as my friend did but i don't have definite info

I guess I need to revise algebraic inequalities stuff like that is very hard to see if you haven't done something similar. I mean that was the only thing I couldn't do so its not that bad. Do you also have q11d) answer? My thing is probably right but the wording (of the question) is kinda weird.

 

[notme123]

bruh youre never gonna get something like this in hsc

tryhard smh

 

[synthesisFR]

bruh youre never gonna get something like this in hsc

tryhard smh

if we do im gonna walk out of that exam and then apply for tafe

 

[kkk579]

I found this question in the JRHS 2023 paper that was upload here recently. I skipped it when I did the practise test, but when I went over it again I still couldn't get it. I asked my teacher and she hasn't gotten it as of yet. Could anyone help with this?

stuff you probably have to use:



I tried subbing in a-> (a^3+1)^(1/3) etc but didn't result in anything useful
i did some other manipulation and got this but I don't think it's useful either:


seems like using expanding LHS doesn't get anywhere useful since there is no way to get to the RHS.

would this q be considered hard?

 

[member 6003]

would this q be considered hard?

Yes it's pretty hard considering my teachers couldn't get it.

 

[kkk579]

Yes it's pretty hard considering my teachers couldn't get it.

Js curious but how hard does inequalities get in the hsc? Harder than that or easier?

 

[member 6003]

Js curious but how hard does inequalities get in the hsc? Harder than that or easier?

definitely easier imo

 

[epicmaths]

Ugh I just had the misfortune of spending 3 hours on this to no avail.

This is harder than a lot of competition problems where Cauchy Schwartz, Jensen's, AM GM HM, bounding arguments etc feature more prominently.

After having had a look at the answers - I can say starting off applying GM\geq HM gives you slightly better chances at intuiting the correct terms to use in the denominator of the HM, but I would still personally have trouble seeing it.

For them to put this at Q14 out of 16 is madness.