Question

2+2^2/3+2^1/3=x then find x^3- 6x^2 + 6x

Answer 1

 x = 2 + 2^(2/3) + 2^(1/3)

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

=(x-2)^3 = [2^(2/3)+2^(1/3)]^3

using (a-b)^3= a^3 - b^3 - 3ab(a-b)

and (a+b)^3= a^3 + b^3 + 3ab(a+b)

 x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)

x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)

 x^3 - 8 -6x^2 + 12x = 6 + 6x - 12

x^3 - 6x^2 +6x = 2