Question

Buna, stie cineva sa rezolve? Va rog

Answer 1

Răspuns:

11. d=x3*(x2*x1-x3^2)-x1*(x1^2-x2*x3)+

x2*(x1*x3-x2^2)=x1*x2*x3-x3^3-x1^3

+x1*x2*x3+x1*x2*x3-x2^3

d=3*x1*x2*x3-x3^3-x1^3-x2^3.

x^3+0*x^2-7*x+2=0;

a=1,b=0,c=-7,d=2;

x1+x2+x3=0=>x1+x2= -x3

x1*x2+x1*x3+x2*x3= -7

x1*x2*x3= -2

x1^2+x2^2+x3^2 =(x1+x2+x3)^2−2×x1×x−2×x1×x3−2×x2×x3=(−b)^2/a^2 −2×c÷a=>x1^2+x2^2+x3^2= -14

x1^3+x2^3+x3^3=-b/a*(x1^2+x2^2+x3^2)

-b/a*(x1^2+x2^2+x3^2)-c/a*(x1+x2+x3)-3*d/a=(-b)^3/a^3

-b/a*(x1^2+x2^2+x3^2)-c/a*(x1+x2+x3)-3*d/a=(-b)^3/a^3 -3*(-b)*c/a^2+3*(-d)/a=>x1^3+x2^3+x3^3 =0-0-6= -6.

d = 3*x1*x2*x3-x3^3-x1^3-x2^3 = 3*(-2)

-(x1^3+x2^3+x3^3) = -6+6=0 => b) 0 .