Question

If ${(a+\frac{1}{a})}^2=3$, then $a^3+\frac{1}{a^3}$ equals ____.

• A. $\frac{10\sqrt{3}}{3}$
• B. $3\sqrt{3}$
• C. $0$
• D. $7\sqrt{7}$

Answer 1

Answer: (C)

$0$

We can write,$(a+\frac{1}{a})=\sqrt{3}$

Lets cube both the sides,

$a^3+\frac{1}{a^3}+3(a+\frac{1}{a})=(\sqrt{3}{)}^3$

$a^3+\frac{1}{a^3}+3\sqrt{3}=3\sqrt{3}$

$a^3+\frac{1}{a^3}=0$