I have a problem, which is not really sure for me. Absolutely, it is about the inequalities!
For , if , then proof that
My proof is like this:
Since , then according to AM-GM, we provide
by QM-AM, we provide
Inserting the first AM-GM inequality, we get
Then, solve it.
I had been inspired by filling the perfect squares so it provides
Is that valid for the proof?
Any comments will be appreciated.