Transforming x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122

  • Thread starter footmath
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In summary, the writer suggests using the equation y=x^{2}-3x to transform x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0 to y^{5}+2y^{2}+47y+122, but there is confusion about how to do so. The writer provides the equation x=3/2+\sqrt{y+9/4} and explains that it does not lead to the desired result when substituted into x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0. Further explanation is requested.
  • #1
footmath
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Hello , please guide me .
How can I transformed the equation [TEX]x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0 [/TEX]to [TEX]y^{5}+2y^{2}+47y+122 [/TEX] ?
I studied a lecture that the writer had written :<< by using [TEX]y=x^{2}-3x[/TEX] we can transformed [TEX] x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0[/TEX] to [TEX]y^{5}+2y^{2}+47y+122 [/TEX] But how ? if in [TEX]y=x^2-3x [/TEX] we obtain [TEX]x[/TEX] by [TEX]y[/TEX] we will have : [TEX]x=3/2+\sqrt{y+9/4}[/TEX] and if we substitute [TEX]x=3/2+\sqrt{y+9/4}[/TEX] in [TEX]x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0[/TEX] we don't have $y^5+2y^2+47y+122$ . please explain it.
Thank you very much
 
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  • #2
footmath, please edit your post to fix your LaTeX. All of your TEX and /TEX tags need to be written in lower case - as tex and /tex (inside square brackets).
 

FAQ: Transforming x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122

How do you transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122?

To transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122, you can use the substitution method. Let y=x-1, then substitute y into the original equation. This will result in y^5+2y^2+47y+122.

What is the purpose of transforming x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122?

The purpose of transforming x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 is to simplify the equation and make it easier to solve. The transformed equation is in a more recognizable form and can be manipulated to find the solution more easily.

Can you transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 without using substitution?

Yes, there are other methods to transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122, such as factoring or using algebraic manipulations. However, the substitution method is the most straightforward and efficient way to transform the equation.

How do you know if the transformation of x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 is correct?

To check if the transformation of x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 is correct, you can substitute a value for x into both equations and see if they give the same result. If they do, then the transformation is correct.

Can you transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 for any value of x and y?

Yes, you can transform x^5-x^4-x^3-x^2-x-1 to y^5+2y^2+47y+122 for any value of x and y, as long as the transformation method is applied correctly. However, the resulting equations may not always have real number solutions for x and y, depending on the original equation and the chosen transformation method.

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