If x= 2+2^1/3+2^2/3, find the value of (x^3-6x^2+6x)

Asked by Anjali Srivastava | 9th Jun, 2016, 03:52: PM

Expert Answer:

begin mathsize 16px style x equals 2 plus 2 to the power of 1 third end exponent plus 2 to the power of 2 over 3 end exponent
rightwards double arrow x minus 2 equals 2 to the power of 1 third end exponent plus 2 to the power of 2 over 3 end exponent space space space space space space space space.... left parenthesis 1 right parenthesis
rightwards double arrow open parentheses x minus 2 close parentheses cubed equals open parentheses 2 to the power of 1 third end exponent plus 2 to the power of 2 over 3 end exponent close parentheses cubed
rightwards double arrow x cubed minus 8 plus 12 x minus 6 x squared equals 2 plus 4 plus 3 open square brackets open parentheses 2 to the power of 1 third end exponent cross times 2 to the power of 2 over 3 end exponent close parentheses open parentheses 2 to the power of 1 third end exponent cross times 2 to the power of 2 over 3 end exponent close parentheses close square brackets
rightwards double arrow x cubed minus 8 plus 12 x minus 6 x squared equals 6 plus 3 open square brackets open parentheses 2 close parentheses open parentheses x minus 2 close parentheses close square brackets space space space space space space.... left square bracket F r m space left parenthesis 1 right parenthesis right square bracket
rightwards double arrow x cubed minus 8 plus 12 x minus 6 x squared equals 6 plus 6 left parenthesis x minus 2 right parenthesis
rightwards double arrow x cubed minus 8 plus 12 x minus 6 x squared equals 6 plus 6 x minus 12
rightwards double arrow x cubed minus 6 x squared plus 12 x minus 6 x equals negative 6 plus 8
rightwards double arrow x cubed minus 6 x squared plus 6 x equals 2 end style

Answered by Rashmi Khot | 10th Jun, 2016, 03:32: PM