Odpowiedź:
[tex]1)\\\\2x^6-5x^5+3x^4=0\\\\x^4(2x^2-5x+3)=0\\\\x^4(2x^2-2x-3x+3)=0\\\\x^4(2x(x-1)-3(x-1))=0\\\\x^4(x-1)(2x-3)=0\\\\x^4=0\ \ \ \ \vee\ \ \ \ x-1=0\ \ \ \ \vee\ \ \ \ 2x-3=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=1\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ 2x=3\ \ /:2\\\\x=0\ \ \ \ \vee\ \ \ \ x=1\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=\frac{3}{2}[/tex]
[tex]2)\\\\9x^3-4x^2-27x+12=0\\\\x^2(9x-4)-3(9x-4)=0\\\\(9x-4)(x^2-3)=0\\\\9x-4=0\ \ \ \ \vee\ \ \ \ x^2-3=0\\\\9x=4\ \ /:9\ \ \vee\ \ \ \ x^2=3\\\\x=\frac{4}{9}\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=\sqrt{3}\ \ \ \ \vee\ \ \ \ x=-\sqrt{3}[/tex]
[tex]3)\\\\x^3+4x^2+x-6=0\\\\x^3-x^2+5x^2-5x+6x-6=0\\\\x^2(x-1)+5x(x-1)+6(x-1)=0\\\\(x-1)(x^2+5x+6)=0\\\\(x-1)(x^2+3x+2x+6)=0\\\\(x-1)(x(x+3)+2(x+3))=0\\\\(x-1)(x+3)(x+2)=0\\\\x-1=0\ \ \ \ \vee\ \ \ \ x+3=0\ \ \ \ \vee\ \ \ \ x+2=0\\\\x=1\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-2[/tex]
