question about inequality proofs (1 Viewer)

[chilli 412]

when doing an inequality proof and we reference AM-GM to prove something, to we have to prove the specific am-gm statement we were using? for example, when solving a question that can be put in the form of AM-GM with n=3, would I be allowed to get it in that form and leave the question as proven or would I then have to prove that (x+y+z)/3 >= cuberoot(xyz)

 

[gamja]

no, I would just write (using AM/GM inequality) next to that final line of working that should be fine!

 

[synthesisFR]

Also, do we need to know AM/GM for n=3 and above? I thought we were only ever going to be assessed on n=2 in the HSC itself.

 

[Trebla]

You will usually be expected to derive the AM-GM results from scratch. Either way, the HSC questions will make that very clear.

The only real mention of AM-GM is as an example of an inequality in the syllabus and even then it is framed as a derivation (with the word "establish") for two non-negative numbers: