Question

If x=1+2^(1/3)+2^(2/3) show that x^3-3x^2-3x-1=0

Answer 1

Answer:

Step-by-step explanation:

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

==> x - 1 = 2^(1/3)+2^(2/3) .......(i)

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

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

==> (x - 1)^3 = 2+ 2^2 + 3.2^((1/3)+(2/3)).(x - 1) [ from (i)]

==> x^3 - 3x^2 + 3x - 1= 6 + 6x - 6

==> x^3 - 3x^2 - 3x - 1=0