Question

Rozwiąż równanie /załącznik/

Answer 1

[tex]x^5+2x^2-4x^3-8x^2+3x+6=0\\\\x^4(x+2)-4x^2(x+2)+3(x+2)=0\\\\(x+2)(x^4-4x^2+3)=0\\\\x+2=0\ \vee \ x^4-4x^2+3=0\\\\\\x^4-4x^2+3=0\ \ , \ \ x^2=t\\\\t^2-4t+3=0\\\\\Delta=4\rightarrow\sqrt{\Delta}=2\\\\[/tex]

[tex]t_1=\frac{4-2}{2}\ \vee \ t_2==\frac{4+2}{2}\\\\t_1=1\ \vee \ t_2=3\\\\\\x+2=0\ \vee \ x^4-4x^2+3=0\\\\x=-2\ \vee \ x^2=1\ \vee \ x_2=3\\\\x_1=-2\ \vee x_2=1\ \vee x_3=-1\ \vee \ x_4=\sqrt{3}\ \vee \ x_5=-\sqrt{3}\\[/tex]