<s>[INST] Solving a biquadratic $x^{4}-2x^3 + x^2 - 2x +1 =0$ How do I find the roots of $$x^{4}-2x^3 + x^2 - 2x +1 =0$$
I am not able to find any roots by trial and error. 
 [/INST] *

*Divide throughout by $x^2$.

*Then you have $x^{2}-2x + 1 - \frac{2}{x} + \frac{1}{x^2} = 0$

*You can re-write as $x^{2}+\frac{1}{x^2} - 2(x+\frac{1}{x}) + 1 =0$

*Then use $x^{2}+\frac{1}{x^2} = (x+\frac{1}{x})^{2} -2$ and then reduce it to a quadratic by putting $y=x+\frac{1}{x}$.
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