If ( a + 1/a )^2\, = 3 then a^3 + 1a^3 = ?

Answer: Option D

$$\begin{array}{rl}& {\left(a+\frac{1}{a}\right)}^2=3\\ & a+\frac{1}{a}=\sqrt{3}\\ & \text{Take cube on both sides}\\ & {\left(a+\frac{1}{a}\right)}^3={\left(\sqrt{3}\right)}^3\\ & \Rightarrow a^3+\frac{1}{a^3}+3.a.\frac{1}{a}\left(a+\frac{1}{a}\right)=3\sqrt{3}\\ & \Rightarrow a^3+\frac{1}{a^3}+3\sqrt{3}=3\sqrt{3}\\ & \Rightarrow a^3+\frac{1}{a^3}=0\end{array}$$