Find the value of this expression

[utkarshakash]

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?

 

[mfb]

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).

 

[AJ Bentley]

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.

 

[HallsofIvy]

You can simplify the calculations a little by writting this as x(6+ x(x- 6)).

 

[Dick]

Try using $x^3-6x^2+6x=(x-2)^3-6x+8$. That actually saves some work.

 

[utkarshakash]

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.