<s>[INST] Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$. 
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that
  $a^2 + b^2 + c^2 \ge a + b + c$.

I'm supposed to prove this use AM-GM, but can't figure it out. Any hints?
 [/INST] since
$$a^2+1\ge 2a$$
so
$$a^2+b^2+c^2+3\ge a+b+c+(a+b+c)\ge a+b+c+3\sqrt[3]{abc}=a+b+c+3$$
so
$$a^2+b^2+c^2\ge a+b+c$$
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