Find 5 different demonstrations (proofs) of the Arithmetic Mean -- Geometric Mean inequality for two non-negative numbers

More algebra. . .

Using some geometry. . .

Can you

generalizethis theorem?

In the case of three positive quantities:

In general,For a discussion of one proof of these generalizations, see Courant, R,. & Robbins, H. (1941)

What is Mathematics?New York: Oxford University Press, pp. 361-365.

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