If $${a^2} + \frac{2}{{{a^2}}} = 16,$$   then find the value of $$\frac{{72{a^2}}}{{{a^4} + 2 + 8{a^2}}}.$$

A. 3

B. 1

C. 4

D. 2

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {a^2} + \frac{2}{{{a^2}}} = 16 \cr & \frac{{72{a^2}}}{{{a^4} + 2 + 8{a^2}}} \cr & = \frac{{72}}{{{a^2} + \frac{2}{{{a^2}}} + 8}} \cr & = \frac{{72}}{{16 + 8}} \cr & = 3 \cr} $$