Suma patratelor radacinilor unei ecuatii de gradul II

Moderators: Laurian Filip, Beniamin Bogosel, Filip Chindea

Post Reply
alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Suma patratelor radacinilor unei ecuatii de gradul II

Post by alex2008 »

Fara a rezolva ecuatia , sa se gaseasca suma patratelor radacinilor ecuatiei : \( (x^2+2x)^2-5(x^2+2x)+3=0 \)
Top
Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Ecuatia este : \( x^4+4x^3-x^2-10x+3=0 \) si conform relatiilor lui Vie'te avem

\( x_1^2+x_2^2+x_3^2+x_4^2=(x_1+x_2+x_3+x_4)^2-2(x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4+x_3x_4)=4^2-2(-1)=18 \)
Top
Post Reply

Return to “Clasa a IX-a”