Question

Salut am si eu nevoie de ajutor la puntul c.Multumesc!

Answer 1

$f = X^3-2X^2-2X+4\\ \\ (x_1+x_2+x_3)\left(\dfrac{1}{x_1}+\dfrac{1}{x_2}+\dfrac{1}{x_3}\right) = \\ \\ = (x_1+x_2+x_3)\left(\dfrac{x_2x_3+x_1x_3+x_1x_2}{x_1x_2x_3}\right)=\\ \\ = -\dfrac{b}{a}\cdot \left(\dfrac{\dfrac{c}{a}}{-\dfrac{d}{a}}\right) =\dfrac{bc}{ad} =\dfrac{-2\cdot (-2)}{1\cdot 4} = \dfrac{4}{4} =\boxed{1}$

Answer 2

Se aplica relatiile lui Viete pentru polinomul de gradul al 3-lea

S₁ =x₁+x₂+x₃ =-a₂/a₃ =2

S₂ =x₁x₂ +x₂x₃ +x₁x₃ =a₁/a₃ =-2

S₃ =x₁x₂x₃ =-a₀/a₃ =-4

Egalitatea de la subpunctul c se scrie echivalent

(x₁+x₂+x₃)( (x₁x₂ +x₂x₃ +x₁x₃)/x₁x₂x₃ )=1 ceea ce trebuia demonstrat.