Question

if x - 1/x = root 3 then find x^3 - 1/x^3

Answer 1

Answer:

Step-by-step explanation:

x - 1/x = sqrt(3)

Then (x - 1/x)^3 = (sqrt(3))^3

          x^3 - 1/x^3 + 2*x*(1/x) ( 1/x  - x) = 3^(3/2)

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

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

          x^3 - 1/x^3  =3^(3/2) + 2 (sqrt(3))

                             =3^3 * 3^(1/2) + 2 * 3^(1/2)

                             =3^(1/2) * (3^3 + 2)

                             =root(3) * (9+2)

                             =11 * root(3)