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Find the value of this expression

  1. Nov 4, 2012 #1


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    1. The problem statement, all variables and given/known data
    If [itex]x=2+2^{2/3}+2^{1/3}[/itex], then the value of [itex]x^3-6x^2+6x[/itex] is

    2. Relevant equations

    3. The attempt at a solution
    The very first idea that comes to my mind is to substitute the value of x in the given expression. But that gets very complicated and long as well. Any other ideas?
  2. jcsd
  3. Nov 4, 2012 #2


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    I don't think you can avoid this. Simplify as early and as much as possible (e.g. calculate x^2, simplify that and multiply with x to get x^3).
  4. Nov 4, 2012 #3
    It doesn't look so bad...
    x3 is easy since 3s cancel a lot. Then x2 isn't too bad because 2*2 +2*1 = 6 which divides by 3 easily.

    It all simplifies nicely as you go along.:smile:
  5. Nov 4, 2012 #4


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    You can simplify the calculations a little by writting this as x(6+ x(x- 6)).
  6. Nov 4, 2012 #5


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    Try using [itex]x^3-6x^2+6x=(x-2)^3-6x+8[/itex]. That actually saves some work.
  7. Nov 6, 2012 #6


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    Thanks. It did save a lot of work.
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