One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3). What are the other two roots?
+14915 One of the roots of x^3 - 5x^2 + 5x - 1 = 0 is 2 - sqrt(3). What are the other two roots?
Hallo Guest
\(I\ assume: x_1 = 1\)
\((x^3 - 5x^2 + 5x - 1):(x-1)=\color{blue}x^2-4x+1\)
\(\underline{x^3\ -\ x^2}\)
\({-4x^2+5x}\)
\(\underline{-4x^2+4x}\)
\(x-1\)
\(\underline{x-1}\)
\(0\)
\(x_1=1\)
\(x^2-4x+1=0\\ x=2\pm\sqrt{4-1}\\ \)
\(x_2=2+\sqrt{3}\\ x_3=2-\sqrt{3}\)
!
