If a4 + 1 = [ a^2 b^2 ] (4b2 - b4 - 1), then what is the value of a4 + b4?

Answer: Option A

$$\begin{array}{rl}& a^4+1=\left(\frac{a^2}{b^2}\right)\left(4b^2-b^4-1\right)\\ & \text{take }a=b=1\\ & 1+1=\frac{1}{1}\left(4-1-1\right)\\ & 2=2\text{ satisfied}\\ & \therefore a^4+b^4=1+1=2\end{array}$$