Odpowiedź:
[tex]1)\\\\x^5-2x^3+x=0\\\\x(x^4-2x^2+1)=0\\\\x(x^2-1)^2=0\\\\x=0\ \ \ \ \vee\ \ \ \ (x^2-1)^2=0\\\\x=0\ \ \ \ \vee\ \ \ \ x^2-1=0\\\\x=0\ \ \ \ \vee\ \ \ \ x^2=1\\\\x=0\ \ \ \ \vee\ \ \ \ x=-1\ \ \ \ \vee\ \ \ \ x=1[/tex]
[tex]2)\\\\x^3+3x^2+2x=0\\\\x(x^2+3x+2)=0\\\\x(x^2+2x+x+2)=0\\\\x(x(x+2)+(x+2))=0\\\\x(x+2)(x+1)=0\\\\x=0\ \ \ \ \vee\ \ \ \ x+2=0\ \ \ \ \vee\ \ \ \ x+1=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=-2\ \ \ \ \ \ \vee\ \ \ \ x=-1[/tex]
[tex]3)\\\\x^4=4x^3+5x^3\\\\x^4=9x^3\\\\x^4-9x^3=0\\\\x^3(x-9)=0\\\\x^3=0\ \ \ \ \vee\ \ \ \ x-9=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=9\\\\\\4)\\\\6x^3+9x^2=3x^4\ \ /:3\\\\2x^3+3x^2=x^4\\\\2x^3+3x^2-x^4=0\\\\-x^4+2x^3+3x^2=0\ \ /\cdot(-1)\\\\x^4-2x^3-3x^2=0\\\\x^2(x^2-2x-3)=0\\\\x^2(x^2+x-3x-3)=0\\\\x^2(x(x+1)-3(x+1))=0\\\\x^2(x+1)(x-3)=0\\\\x^2=0\ \ \ \ \vee\ \ \ \ x+1=0\ \ \ \ \vee\ \ \ \ x-3=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=-1\ \ \ \ \ \ \ \ \vee\ \ \ \ x=3[/tex]