Question

if x-2=2²/³+2¹/³,show that x³-6x²+6x-2=0

Answer 1

what is the question it's not proper

or

I didn't understand

the first part

Answer 2

Given that x = 2 + 2^(2/3) + 2^(1/3)
so x - 2 = 2^(2/3) + 2^(1/3)
=(x-2)^3 = [2^(2/3)+2^(1/3)]^3
use (a-b)^3= a^3 - b^3 - 3ab(a-b)
and (a+b)^3= a^3 + b^3 + 3ab(a+b) formulae.
or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2