Solution
Given : $$(a+\frac{1}{a})^2=3$$
=> $$(a+\frac{1}{a})=\sqrt3$$ -----------(i)
Cubing both sides, we get :
=> $$(a+\frac{1}{a})^3=(\sqrt3)^3$$
=> $$a^3+\frac{1}{a^3}+3(a)(\frac{1}{a})(a+\frac{1}{a})=3\sqrt3$$
=> $$a^3+\frac{1}{a^3}+3(\sqrt3)=3\sqrt3$$ [Using (i)]
=> $$a^3+\frac{1}{a^3}=3\sqrt3-3\sqrt3=0$$
=> Ans - (A)
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