Question

If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]

Options

• 64

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• 8

• 2

Answer 1

In the given problem, we have to find the value of  `x^3+1/x^3`

Given  `x+ 1/x = 2`

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

Here putting `x+ 1/x = 2`, 

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

             `(2)^3 = x^3 + 1/x^3 + 3 (x xx 1/x )(2)`

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

           ` 8-6 = x^3 + 1/x^3`

                  ` 2= x^3 + 1/x^3`

Hence the value of  `x^3 + 1/x^3` is  2.