If x - (1 / x) = 3 then what will be the value of x³ - (1 / x³) ?

Solution: 

To solve this, we will use algebraic identity of a³ - b³ .

Let's find the value of x³ - (1 / x³).

Given x - (1 / x) = 3 

By using the algebraic identity (a - b)³ = a³ - b³ - 3 ab (a - b) on LHS, we get

x³ - (1 / x³) - 3x × 1/x [ x - (1 / x)] = (3)³

x³ - (1 / x³) - 3(3) = 27

x³ - (1 / x³) = 27 + 9

x³ - (1 / x³) = 36.

Thus, the value of x³ - (1 / x³) is 36.

If x - (1 / x) = 3 then what will be the value of x³ - (1 / x³) ?

Summary:

The value of x³ - (1 / x³) is 36.