I had a question in my exam and they asked to prove that prove that:
$$3(1+a^2+a^4)\geq(1+a+a^2)^2$$ for all $a\in\mathbb R$.
Now , I solved it , but the problem is that in the answer they wrote this: using Chebyshev inequality:
$$(1+a+a^2)^2=(1·1+a·1+a^2·1)^2≤(1+a^2+a^4)·(1+1+1)=3(1+a^2+a^4).$$ And so I tried searching the web for this inequality but all it found was the Chebyshev's inequality for probabillity. can someone please send me link regarding this inequality or just write it here?