If $a+\frac{1}{a}=\sqrt{3}$, then find the value of $a^{3}+\frac{1}{a^{3}}$.
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If $a+\frac{1}{a}=\sqrt{3}$, then find the value of $a^{3}+\frac{1}{a^{3}}$.

(a) 1

(b) 0

(c) 2

(d) 3
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Best Answer

Solution :

 $a^{3}+\frac{1}{a^{3}}$

$=\left(a+\frac{1}{a}\right)^{3}-3 \times a \times \frac{1}{a}\left(a+\frac{1}{a}\right)$

$=\left(a+\frac{1}{a}\right)^{3}-3 \times\left(a+\frac{1}{a}\right)$

$=(\sqrt{3})^{3}-3 \times \sqrt{3}$

$=3 \sqrt{3}-3 \sqrt{3}=0 ;$ Ans.

So, the correct option  $is$ (b)

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