a)
x1²+x2²+x3²=(x1+x2+x3)²-2(x1x2+x2x3+x3x1)= (Viete)= (-(-3))²-2*m=9-2m
as simple as that!
x1=x2=x3
x1+x2+x3=3x1=-(-3)/1=3/1=3
3x1=3
x1=1
f=(x-x1)³=(x-1)³=x³-3x²+3x-1=x³-3x²+mx+n
identificand coeficientii, obtinem
3=m
-1=n
deci
m=3
si
n=-1
as tricky as that!
c)
x³-3x²+x-3=x²(x-3)+(x-3)=(x-3) (x²+1)=(x-3) (x²-(-1))=
(x-3)(x²-i²)=(x-3) (x-i)(x+i), unde i²=-1
as strange as that!!!
