Quoting from Arthur Engel's "Problem Solving Strategies":

To the part inred, how is this possible? If keeps increasing, has to decrease in order to keep the product of and constant at .

To the part inblue, I don't get this.

To the part ingreen, 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 ?