2.
b)
f = [tex](X+1)( X^{2}-X+1) + 2X(X+1) [/tex]
f = [tex](X+1)( X^{2} +X+1)[/tex]
c) Ne folosim de relatiile lui Viete.
[tex] x_{1} + x_{2} + x_{3} = \frac{-b}{a} = -2[/tex]
[tex] x_{1} x_{2} + x_{2} x_{3} + x_{1} x_{3} = \frac{c}{a} = a[/tex]
[tex] x_{1} x_{2} x_{3} = \frac{-d}{a} = -b[/tex]
[tex]x_{1} ( x_{1} -1)+ x_{2} ( x_{2} -1) + x_{3} ( x_{3} -1) = -2[/tex]
[tex] x_{1} ^{2} - x_{1} + x_{2} ^{2} - x_{2} + x_{3} ^{2} - x_{3} = -2[/tex]
[tex]x_{1} ^{2} + x_{2} ^{2}+x_{3} ^{2} - ( x_{1}+ x_{2}+x_{3}) = -2[/tex]
[tex]x_{1} ^{2} + x_{2} ^{2}+x_{3} ^{2} = 4-2a[/tex] ( obtinem aceasta relatie ridicand prima relatie a lui Viete la patrat).
[tex]x_{1}+ x_{2}+x_{3} = -2[/tex]
⇒ [tex]4-2a-(-2)=-2[/tex]
⇒ [tex]6-2a=-2[/tex] ⇒ [tex]a=4[/tex]
