Question

Exercițiul 2,va rog!!!!

Answer 1

f=x⁴-x²+x-1

Scriem relatiile lui Viete:

$x_1+x_2+x_3+x_4=-b/a=0/1=0$

$x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4+x_3x_4=c/a=-1/1=-1$

$x_1x_2x_3+x_1x_2x_4+x_1x_3x_4+x_2x_3x_4=-d/a=-1/1=-1$

$x_1x_2x_3x_4=e/a=-1/1=-1$

a)

S₁=x₁+x₂+x₃+x₄=-b/a=0/1=0

b)

f=x⁴

x⁴-x²+x-1=x⁴

-x²+x-1=0

Δ=1²-4*(-1)*(-1)=1-4=-3=3i²

x1=(-1+i√3)/2

x2=(-1-i√3)/2

c)

$\frac{1}{x_1}+\frac{1}{x_2} +\frac{1}{x_3} +\frac{1}{x_4}=\frac{x_2x_3x_4+x_1x_3x_4+x_1x_2x_4+x_1x_2x_3}{x_1x_2x_3x_4} =\frac{-1}{-1} =1$