If x(3 - 2/x ) = 3/x , then the value of x³ - 1/x³ is equal to:

If x(3 - 2/x ) = 3/x , then the value of x³ - 1/x³ is…

If x(3 - $\frac{2}{x}$ ) = $\frac{3}{x}$ , then the value of x³ - 1/x³ is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{62}{27}$

Here it is given that,

x(3 - $\frac{2}{x}$ ) = $\frac{3}{x}$

3x - 2 = 3/x

3x - 3/x = 2

x - 1/x = 2/3

On cubing both sides we get,

x³ - 1/x³ - 3 × x × 1/x (x - 1/x) = 8/27

x³ - 1/x³ - 2 = 8/27

x³ - 1/x³ = 8/27 + 2

x³ - 1/x³ = 62/27.