Hi, I'm a little stuck on this question.

Part a) asks to prove that , where is the diagonal of a rectangular brick with sides of length a, b and c.

I've already proved that, by saying:

The question I'm struggling with is part b), which says "If V denotes the volume of the brick, show that .

I've found the AM by letting then dividing by 3 and raising to the power of to get .

I'm not sure what to do when finding the AM/GM inequality as I can't find a way to make GM = the volume (which is the only way I can think to solve this at the moment).

So far I've got , but I can't make any progress from there.

Is it as simple as ? Just seems to me like there is a neater solution and I've made some sort of formulaic or calculative error.

Appreciate any input.