Finding the Maximum Value of n for a Given Equation

[Marcelo Arevalo]

What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?

 

[MarkFL]

I think you will agree that:

$$n^2<n^2+\frac{2016}{n^2}$$

So, how can some number be smaller than the smaller value, and at the same time greater than the greater value?

 

[Marcelo Arevalo]

Meaning, there's no such thing as the smaller value, and at the same time greater than the greater value?