Subject of a future side-book / short story; one of the words has already appeared in the series.
Back in 2010, before the final book was written, Paolini said the book would feature them.
How will Brom’s seven words to Eragon show up in the fourth book, also I think Solumbum’s riddle will come in again, right?
Christopher Paolini: You’ll have to read Book Four in order to find out what happens with Brom’s seven words and Solembum’s riddle.
Random Buzzers Q&A with Christopher Paolini 2010
However he didn't end up fitting them in and so decided he would tackle it in a short story.
Let’s talk about Brom’s “seven words”. There are fan theories on both sides of the aisle here — they’re either seven regular words of no real importance, given to Eragon to help him survive the next few weeks (my personal favorite) or they were seven powerful words that Eragon never got around to using. Were these included in the books without mention, or something else entirely?
Christopher Paolini: There is a mention of one of the words (a death word) in either Eldest or Brisingr. However, the words didn’t have a role to play in this series. I tried to find a place to fit them in, but there wasn’t any. Eragon doesn’t use words to defeat Galbatorix, and the one place where it might have made sense to draw upon them (the hallway going into the throne room) Eragon uses what Oromis taught him about teleportation to defeat Galbatorix’s traps. So, a long time ago, I decided to address the seven words separately, in a short story aside from the main series. Again, as I said before, Eragon is going to live a very long time, and the events in the cycle are only at the very beginning of his life.
Shurtugal.com - First Post-Inheritance Interview with Christopher
In 2018 he confirmed that this will not appear in Book V, but in one of the spin-off books.
Before Brom died he whispered 7 words at Eragon. Will they be mentioned in book V?
Christopher Paolini: They're a subject of another book (not Book V, lol).
Currently, Christopher is publishing his short stories through a spin-off series titled "Tales from Alagaësia". It wasn't in the first volume and isn't one of the two stories he's said will be in the second volume, so we can assume it'll be in the third volume or later.
- We don't know
- It wasn't mentioned in any of the published books
- It will not be covered in Book V
- There will be a short story written about it, probably in one of the Tales from Alagaësia volumes, (#3 or later)
- One of the words was already mentioned in print, as a death word in Eldest or Brisingr.