Question

if x=2+2^(1/3)+2^(2/3) then find x^3-6x^2+6x-2​

Answer 1

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

={2^3+2+2^2} -6{2^2+2^2/3+2^4/3}+6(2+2^1/3+2^2/3)-2

={8+2+4}-6{4+2^2/3+2^4/3}+6(2+2^1/3+2^2/3)-2

=14-24+(12^2/3)+(12^4/3)+12+(12^1/3)+(12^2/3)-2

={14-24+12-2}+{12^2/3+12^4/3+12^1/3+12^2/3}

=0+{12^2/3+4/3+1/3+2/3}

=12^3

=1728