Question

If x=a^1/3-a^-1/3 then x^3+3x-a is.......?.

Answer 1

x = (a^1/3) - (a^-1/3)
Cubing on both sides,
x^3 = (a^1/3)^3 - (a^-1/3)^3 - 3(a^1/3 - a^-1/3)
x^3 = a - a^-1 - 3x
x^3 + 3x - a= a - a^-1 - 3x + 3x - a
                    = – a^–1

Answer 2

2a^1/3 + 2a^-1/3 - a^-1