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,

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

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

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

$y^3=6y+6$

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

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