My teacher gave me this problem:
\(a\), \(b\) and \(c\) are three positives such that \(abc = 1\). Prove that
Here's how I solve it.
(Fun fact, the Sedrakyan's inequality is called the Schwarz inequality here.)
Let , we have that and .
The problem becomes:
Calculate the maximum value of the following expression if .
So if you can:
solve the next part of the solution
(prove that there is no maximum value of and) solve the original problem in a faster, more convenient way
then feel free to write them in the comments' section. Please help me!