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

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SUMMARY

The transformation of the polynomial equation x5 - x4 - x3 - x2 - x - 1 = 0 to y5 + 2y2 + 47y + 122 is achieved using the substitution y = x2 - 3x. This method simplifies the original equation, but the correct substitution process must be followed to ensure the transformation yields the desired polynomial. The discussion highlights the importance of accurately substituting x in terms of y and emphasizes the need for precise mathematical notation in LaTeX.

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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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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).
 

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