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Verified answer

х⁴-3х³+4х²-9х+3=(x^2+3)*(x^2-3x+1)

x^2+3=0

x^2=-3

x^2-3x+1=0

D=(-3)^2-4*1*1=5

x1=3+корень5/2
x2=3-корень5/2

Ответ:  x1,2=3+корень5/2;  3-корень5/2