Question

If $a=x+\frac{1}{x},$ then $(x^3+x^{-3})$ is equal to

• A. $a^3+3a$
• B. $a^3-3a$
• C. $a^3+3$
• D. $a^3-3$

Answer 1

Answer: (B)

$a^3-3a$

Formula: $(a+b{)}^3=a^3+3ab(a+b)+b^3$

$\Rightarrow a=x+\frac{1}{x}$

Taking cube on both the side

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

$\therefore a^3=x^3+\frac{1}{x^3}+3a$

$\therefore x^3+\frac{1}{x^3}=a^3-3a$