X^4-3x^3+x^2+3x-2=0

[latex] x^{4}-3 x^{3}+ x^{2} +3x-2=0 \\ (x^{4}-1 )+ (x^{2} -1)-(3 x^{3}-3x)=0 \\ ( x^{2} -1)( x^{2} +1)+( x^{2} -1)-3x( x^{2} -1)=0 \\ ( x^{2} -1)( x^{2} +1+1-3x)=0 \\ x^{2} -1=0 =\ \textgreater \ (x-1)(x+1)=0 \\ x1=1 \\ x2=-1  [/latex] или [latex] x^{2} -3x+2=0 \\ D=9-8=1 \\ x3= \frac{3+1}{2} =2 \\ x4= \frac{3-1}{2}=1[/latex] Ответ: x1=1 ; x2=-1 ; x3=2