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 = extgreater (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