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Rezolvati va rog frumos : ( dau 100 de puncte !)

a) [tex] x^{3} / ( x^{2} -4 ) - x / (x-2 ) + 2/ (x+2 )[/tex]

b) efectuati impartirea polinomului P (x ) la polinomul Q(x) :
P (x) = 4 x^{4} + x^{2} -1 , iar Q (x) = x^{2} -1


Răspuns :

a) x^3/(x^2-4)-x/(x-2)+2/(x+2)=0

x^2-4=(x-2)(x+2)
Aduci ecuatia la acelasi numitor.

x^3+(−x)(x+2)+2(x−2)=0
x^3x^2−4=0
(x−2)(x^2+x+2)=0
x-2=0 => x=2 dar nu convine
x^2+x+2=0 => Δ<0 => x nu aparține lui ℝ (insa exista solutii in ℂ)

b) P(x)= 4x^3 + x^2 - 1
    Q(x)= x^2 - 1
http://i.imgur.com/uYnuJ0M.png