Find the value of #x^3-6x^2+6x # when # x=2+2^(2/3)+2^(1/3)?#

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Answer 1 · 2018-06-20T10:45:44

#2#

#x^3-6x^2+6x#

=#x^3-6x^2+12x-8-6x+12-4#

=#(x-2)^3-6*(x-2)-4#

After setting #y=x-2#, this equation became #y^3-6y-4#

Hence,

#y=2^(2/3)+2^(1/3)#

#y^3=4+6*2^(2/3)+6*2^(1/3)+2#

#y^3=6+6*(2^(2/3)+2^(1/3))#

#y^3=6y+6#

#y^3-6y-4=2#