решите уравнение х³-8х²+8х-1

x³-8x²+8x-1=x³-1-8x²+8x=(x³-1)-8x(x-1)=
=(x-1)(x²+x+1)-8x(x-1)=(x-1)(x²+x+1-8x)=
=(x-1)(x²-7x+1)

x²-7x+1=(x-3,5-1,5√5)(x-3,5+1,5√5)
(D=49-4=45=9.5, √D=√(9.5)=√9.√5=3√5)
Uravnenie x³-8x²+8x-1=0 imeet korni:
x1=1, x2=3,5+1,5√5, x3=3,5-1,5√5