Question

If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]

Answer 1

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

Given  `x+1/x = 5`

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

Here putting, `x+1/x = 5`,`

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

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

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

               `125 = x^3 + 1/x^3 + 3 xx 5 `

              `125 = x^3 + 1/x^3 +1 5 `

      `125 -15 = x^3 + 1/x^3` 

               `110 = x^3 + 1/x^3`

Hence the value of  `x^3 +1/x^3`is 110