Question

Descompuneti in factori: 3n^2-2n+1.

Answer 1

Liceu
 3(n-n1 )(n-n2) unde n1 si n2 sunt radacinile ecuatiaei
3n²-2n+1=0
Δ=4-12=-8 <0, n1,2∉R, expresia estre ireductibila inR, nu se poate descompune in factori de grad 1 cu coeficienti reali


altfel
3n²-2n+1/3+2/3=
3n²-2n+(1/√3)²+2/3=(n√3-1/√3)²+2/3≥0 ∀n∈R

Se poate descompune insa in C
n1,2=[2+-√(-8)]/6= [2+- i2√2]/6= (1+-i√2)/3


3n^2-2n+1.= 3[n-(1-i√2)/3][n-(1+i√2)/3]
                     (1/3) *    [3n-(1-i√2)][3n-(1+i√2)]