Question

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

Options

• 5

• 10

• 15

• none of these

Answer 1

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

Given  `x^3 + 1/x^3 = 110`

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 = 5 in the above equation we get

                 `(5)^3 = x^3 + 1/x^3 + 3(5)`

                   `125 = x^3 + 1/x^3 + 15`

          `125 - 15 = x^3 + 1/x^3`

                    `110 = 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 = 110`

Hence the value of  `x+ 1/x` is 5.