If x=2-2^1/3 +2^2/3, then the value of x^3 - 6x^2 +18x +18 is

• x^3 - 6x^2 +18x +18 = [x^3 + 3*(x^2)*(-2) + 3*(x)*{(-2)^2} + (-2)^3 ] + 6x + 26
  = (x-2)^3 + 6x + 26..........[(eqn1)]
  Now, from the given data x-2 = [2^(2/3)- 2^(1/3)]
  => (x-2) = {2^(1/3)}[2^(1/3)- 1]
  => (x-2)^3 = [{2^(1/3)}^(3)][2^(1/3)- 1]^3
  => (x-2)^3 = 2[2+ {3*(2^(2/3))(-1)} + {3*(2^(1/3))*(-1)^(2)}+ (-1)^(3)]
  => (x-2)^3 = 2 - 6*(2^(2/3)) + 6*(2^(1/3))
  => (x-2)^3 = 2 - 6*[(2^(2/3))- (2^(1/3)]
  => (x-2)^3 = 2 - 6*(x-2)
  => (x-2)^3 = -6*x +14
  => (x-2)^3 + 6*x -14 =0
  => (x-2)^3 + 6*x -14 + 40 = 40
  => (x-2)^3 + 6x + 26 = 40
  So, we get [(eqn1)] = 40
  So, x^3 - 6x^2 +18x +18 =40..
  
  So, Answer is
  x^3 - 6x^2 +18x +18 =40..
• 12 years agoHelpfull: Yes(11) No(1)