Find the value of this expression

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Homework Help Overview

The problem involves evaluating the expression x^3 - 6x^2 + 6x, where x is defined as 2 + 2^{2/3} + 2^{1/3}. The discussion centers around simplifying this expression and exploring various methods of calculation.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different strategies for simplifying the expression, including direct substitution and algebraic manipulation. Some express concern about the complexity of direct substitution, while others suggest breaking down the calculations into simpler parts.

Discussion Status

Several participants have offered different approaches to simplify the expression, with some finding success in their methods. There is an ongoing exploration of various simplification techniques, and while no consensus has been reached, productive suggestions have been made.

Contextual Notes

Participants are navigating the complexity of the expression and considering the implications of their chosen methods. The discussion reflects a range of interpretations and strategies without resolving the problem completely.

utkarshakash
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Homework Statement


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

Homework Equations



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?
 
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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).
 
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:
 
You can simplify the calculations a little by writting this as x(6+ x(x- 6)).
 
Try using x^3-6x^2+6x=(x-2)^3-6x+8. That actually saves some work.
 
Dick said:
Try using x^3-6x^2+6x=(x-2)^3-6x+8. That actually saves some work.

Thanks. It did save a lot of work.
 

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