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

[evagelos]

By using appropriate theorems derive the following statement :

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

 

[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).