If $${a^3} + \frac{1}{{{a^3}}} = 2{\text{,}}$$   then the value of $$\frac{{{a^2} + 1}}{a}$$  is (a positive number) ?

$$\eqalign{ & {\text{But }}a = 1 \cr & {a^3} + \frac{1}{{{a^3}}} = 2 \cr & \Rightarrow {1^3} + \frac{1}{{{1^3}}} = 2 \cr & \Rightarrow 2 = 2{\text{ }}\left( {{\text{Satisfy}}} \right) \cr & {\text{So, }}\frac{{{a^2} + 1}}{a} \cr & = \frac{{{1^2} + 1}}{1} \cr & = 2 \cr} $$