Question

решите уравнение x^5 + x^4 - x^3 - x^2 - 6x - 6 = 0

Answer 1

$x^5+x^4-x^3-x^2-6x-6=0\\x^4(x+1)-x^2(x+1)-6(x+1)=0\\(x+1)(x^4-x^2-6)=0\\a); ; x+1=0; ; to ; ; x_1=-1\\b); ; x^4-x^2-6=0; ,; ; t=x^2 geq 0; ; Rightarrow ; ; t^2-t-6=0; ,\\t_1=-2,; t_2=3; ; (teorema; Vieta)\\t^2-t-6=(t+2)(t-3)=0\\(x^2+2)(x^2-3)=0\\(x^2+2)(x-sqrt3)(x+sqrt3)=0; ; Rightarrow ; ; x_2=-sqrt3; ,; x_2=sqrt3\\Otvet;; ; -sqrt3; ,; -1; ,; sqrt3; .$