How can I use theorems to derive a statement about inequalities?

Thread starter evagelos
Start date Nov 27, 2009
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deriving

AI Thread Summary

The discussion focuses on deriving the inequality a^2 + b^2 + c^2 ≥ ab + bc + ac using established theorems and identities. Participants suggest leveraging the properties of squares, such as (a-b)^2 ≥ 0, (b-c)^2 ≥ 0, and (a-c)^2 ≥ 0, to support the derivation. The AM-GM inequality is also recommended for use with pairs of variables to reinforce the argument. The conversation emphasizes the importance of these mathematical tools in proving the stated inequalities. Overall, the thread highlights methods for applying theorems to establish relationships between variables in inequalities.

Nov 27, 2009

evagelos

By using appropriate theorems derive the following statement :

a^2 + b^2 + c^2\geq ab + bc +ac

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Nov 27, 2009

rasmhop

(a-b)^2 \geq 0
(b-c)^2 \geq 0
(a-c)^2 \geq 0
Try using these identities to derive your statement. Or if you've learn about the AM-GM inequality, then use it one two variables on the right at a time (this is the same as using the identities above).

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