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One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3).  What are the other two roots?

 Dec 5, 2019
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One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3).  What are the other two roots?

 

Hallo Guest

 

\(I\ assume: x_1 = 1\)

 

 \((x^3 - 5x^2 + 5x - 1):(x-1)=\color{blue}x^2-4x+1\)

  \(\underline{x^3\ -\ x^2}\)

         \({-4x^2+5x}\)

         \(\underline{-4x^2+4x}\)

                          \(x-1\)

                          \(\underline{x-1}\)

                                  \(0\)

 \(x_1=1\)

 

 \(x^2-4x+1=0\\ x=2\pm\sqrt{4-1}\\ \)

\(x_2=2+\sqrt{3}\\ x_3=2-\sqrt{3}\)

 

laugh  !

 Dec 5, 2019

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