If a^3 + 1a^3 = 2 , then the value of a^2 + 1a is (a positive number) ?

Answer: Option B

$$\begin{array}{rl}& \text{But }a=1\\ & a^3+\frac{1}{a^3}=2\\ & \Rightarrow 1^3+\frac{1}{1^3}=2\\ & \Rightarrow 2=2\left(\text{Satisfy}\right)\\ & \text{So, }\frac{a^2+1}{a}\\ & =\frac{1^2+1}{1}\\ & =2\end{array}$$