Solving x=2+2 2/3 +2 1/3: A Puzzling Challenge

  • Thread starter Thread starter 1/2"
  • Start date Start date
  • Tags Tags
    Challenge
Click For Summary

Homework Help Overview

The problem involves determining the value of x given the equation x = 2 + 2 2/3 + 2 1/3, and subsequently solving the cubic equation x^3 - 6x^2 + 6x - 2 = 0.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss various attempts to substitute values and manipulate the cubic equation, with some expressing confusion about the connections between the two statements. Questions arise regarding the choice of manipulating the expression x - 1 and the rationale behind certain algebraic steps.

Discussion Status

The discussion includes attempts to clarify the problem's requirements and the nature of the solution sought. Some participants suggest that the original poster may be trying to demonstrate that the calculated value of x is a root of the cubic equation, rather than solving it outright. There is no explicit consensus on the approach to take, but several lines of reasoning are being explored.

Contextual Notes

There is a noted concern about the complexity of the calculations involved, with some participants expressing apprehension about large numbers. Additionally, the phrasing of the problem has led to confusion regarding the relationship between the value of x and the cubic equation.

1/2"
Messages
98
Reaction score
0

Homework Statement


The problem is
If x= 2+2 2/3 +2 1/3
solve
x 3-6x 2+ 6x-2 =0


Homework Equations



The Attempt at a Solution


First i tried to substitute the values but its turning out to be really big( and i get quite scared when it turns up like this and so i didn't go any further this way)
then I tried to make a cube of x-1
Like this
x3 -1 -3x 2+ 3x-3x 2+3x-1+x 3=0
<==>(x-1)3+(x-1)3=x 3
<==>2(x-1)3=x 3
Well I can't get any further!
Happy if anyone helps!
 
Last edited:
Physics news on Phys.org
There's something screwy in your problem description. It's akin to saying "If x = 3, how many things are in a dozen?" There doesn't seem to be any connection between the two statements. Are we supposed to assume that x = 2 + 22/3 + 21/3 is a solution of the second equation?
 
1/2" said:

Homework Statement


The problem is
If x= 2+2 2/3 +2 1/3
solve
x 3-6x 2+ 6x-2 =0


Homework Equations



The Attempt at a Solution


First i tried to substitute the values but its turning out to be really big( and i get quite scared when it turns up like this and so i didn't go any further this way)
then I tried to make a cube of x-1
Why did you pick x - 1? I can't think of any good reason to do this.

Also, I have no idea of what you're trying to do in the work below.
1/2" said:
Like this
x3 -1 -3x 2+ 3x-3x 2+3x-1+x 3=0
<==>(x-1)3+(x-1)3=x 3
<==>2(x-1)3=x 3
Well I can't get any further!
Happy if anyone helps!
 
1/2" said:

Homework Statement


The problem is
If x= 2+2 2/3 +2 1/3
solve
x 3-6x 2+ 6x-2 =0

I presume you mean "show", not "solve". You are trying to show that value of x is a root of the cubic.

Homework Equations



The Attempt at a Solution


First i tried to substitute the values but its turning out to be really big( and i get quite scared when it turns up like this and so i didn't go any further this way)
then I tried to make a cube of x-1
Like this
x3 -1 -3x 2+ 3x-3x 2+3x-1+x 3=0
<==>(x-1)3+(x-1)3=x 3
<==>2(x-1)3=x 3
Well I can't get any further!
Happy if anyone helps!

I think you just quit too soon.
2 = \left (\frac {x}{x-1}\right)^3
\frac x {x-1} = 2^{\frac 1 3}

Solve for x:

x = \frac{2^{\frac 1 3}}{2^{\frac 1 3}-1}

Now all you have to do is show this is equal to 2+2 2/3 +2 1/3
 

Similar threads

Replies
8
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
19
Views
3K