Question

If $x-\frac{1}{x} = 3$, then the value of $x^3-\frac{1}{x^3}$ is

• A. 36
• B. 63
• C. 99
• D. None of these

Answer 1

Answer:

A. 36

Solution:

Given:

$x-\frac{1}{x} = 3$

Concept used:

a³ - b³ = (a - b)³ + 3ab(a - b)

Calculation:

$x^3-\frac{1}{x^3}=(x-\frac{1}{x})^3+3\times{x}\times{\frac{1}{x}}\times{(x-\frac{1}{x})}$

$⇒(x-\frac{1}{x})^3+3(x-\frac{1}{x})$

$⇒(3)^3+3\times{3}$

⇒ 27 + 9 = 36

∴ The value of is $x^3-\frac{1}{x^3}$ 36.