<s>[INST] Inequality. $a^2+b^2+c^2 \geq a+b+c$ Let $a,b,c$ be positive real numbers such that $abc=1$. Prove that 
$a^2+b^2+c^2 \geq a+b+c$. 
Thanks
 [/INST] Note that   $$a+b+c≥3,  \tag{1}$$ by AM-GM inequality
Now, by Titu's lemma   $$a^2+b^2+c^2 ≥\frac{(a+b+c)^2}3 ≥ \frac{(a+b+c)^2}{a+b+c}$$   by using  (1)
then $$a^2+b^2+c^2 ≥a+b+c$$   Q.E.D. 
</s>