Question

If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]

 

Options

• 5

• 4

• 3

• 2

Answer 1

In the given problem, we have to find the value of  `x-1/x`

Given  `x^3 - 1/x^3 = 14`

We shall use the identity `(a-b)^3 = a^3 -b^3-3ab (a-b)`

`(x-1/x)^3 = x^3 - 1/x^3 - 3 xx x xx 1/x(x-1/x)`

`(x = 1/x)^3 = x^3 - 1/x^3 -3 (x-1/x)`

Put   `x- 1/x = y` we get,

 `(y)^3 = x^3 -1/x^3 -3(y)`

Substitute y = 2 in above equation we get,

`(2)^3 = x^3 -1/x^3 - 3 (2) `

     `8 = x^3 - 1/x^3 -6`

`8+6 = x^2 -1/x^3`

    `14 = x^3 - 1/x^3`

The Equation `(y )^3 = x^3 - 1/x^3 -3(y)`satisfy the condition that  `x^3 - 1/x^3 = 14`

Hence the value of  `x - 1 /x`is 2