Consider the following for the next two (02) items that follow :

Let $x=\frac{\sin ^2 A+\sin A+1}{\sin A}$ where 0 < A ≤ $\frac{\pi}{2}$

At what value of A does x attain the minimum value ?

Consider the following for the next two (02) items that follow :

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

What is the nature of the triangle ? 

Consider the following for the next two (02) items that follow :

In the triangle ABC, 

a² + b² + c² = ac + √3 bc

If c = 8, what is the area of the triangle ?

Consider the following for the next two (02) items that follow :

Consider the function

f(x) = |x - 2| + |3 - x| + |4 - x|, where x ∈ R.

At what value of x does the function attain minimum value ?