TITLE: What is AM-CM inequality?
QUESTION [6 upvotes]: There's AM-GM inequality. But I've bumped into AM-CM inequality in official solutions for IMO 2018 problems. Here:

This is A7 problem, solution 1 from here: https://www.imo-official.org/problems/IMO2018SL.pdf
I attempted to use AM-GM inequality in case they simply misspelled, but AM-GM doesn't seem to work here.
Any ideas?

REPLY [4 votes]: The AM-CM inequality likely denotes the Arithmetic mean - Cubic mean inequality which is a specific instance of the Generalized mean inequality. This inequality follows directly from Jensen's inequality mentioned in other answers.