Question

Subiectul 2 Exercitiul 2 punctul c cel cu polinom. Se face o substituie dar nu stiu cum la radacini. Va rog explicati amanuntit!

Answer 1

$f = X^3+X-2\\ \\ g = X^3-S_1X^2+S_2X-P \\ \\\\ S_1 = \dfrac{1}{x_1}+\dfrac{1}{x_2}+\dfrac{1}{x_3} = \dfrac{x_1x_2+x_1x_3+x_2x_3}{x_1x_2x_3}=\dfrac{1}{2} \\ \\ S_2 = \dfrac{1}{x_1x_2}+\dfrac{1}{x_2x_3}+\dfrac{1}{x_1x_3} = \dfrac{x_1+x_2+x_3}{(x_1x_2x_3)^2}=0\\\\ P = \dfrac{1}{x_1x_2x_3} = \dfrac{1}{2}\\ \\ \\g =X^3-\dfrac{1}{2}X^2-\dfrac{1}{2}\Bigg|\cdot 2 \\ \\ g = 2X^3-X^2-1 \\ \\ \Rightarrow a = 2,\quad b = -1,\quad c = 0,\quad d = -1$