Quoting from Arthur Engel's "Problem Solving Strategies":
To the part in red, how is this possible? If keeps increasing, has to decrease in order to keep the product of and constant at .
To the part in blue, I don't get this.
To the part in green, isn't harmonic and arithmetic mean equal in magnitude always?
Thanks. Also I don't get the inequality which he has generated. What is he trying to show by ?