Odpowiedź:
[tex]1.\\\\x^3-2x^2+3x=0\\\\x(x^2-2x+3)=0\\\\x=0\ \ \ \ \vee\ \ \ \ x^2-2x+3=0\\\\x=0\ \ \ \ \vee\ \ \ \ \Delta=b^2-4ac=(-2)^2-4*1*3=4-12=-8\\\\x=0\ \ \ \ \vee\ \ \ \ \Delta<0\ \ brak\ \ rozwiazania\\\\Odp.\ \ x=0[/tex]
[tex]2.\\\\x(x^3+27)(x^2-16)(x^2+4)=0\\\\x=0\ \ \ \ \vee\ \ \ \ x^3+27=0\ \ \ \ \vee\ \ \ \ x^2-16=0\ \ \ \ \vee\ \ \ \ x^2+4=0\\\\x=0\ \ \ \ \vee\ \ \ \ x^3=-27\ \ \ \ \ \ \ \ \vee\ \ \ \ x^2=16\ \ \ \ \vee\ \ \ \ x^2=-4\ \ brak\ \ rozwiazania\\\\x=0\ \ \ \ \vee\ \ \ \ x^3=(-3)^3\ \ \ \ \ \ \vee\ \ \ \ x=-4\ \ \ \ \vee\ \ \ \ x=4\\\\x=0\ \ \ \ \vee\ \ \ \ x=-3\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-4\ \ \ \ \ \ \vee\ \ \ \ x=4[/tex]
[tex]3.\\\\x^3-19x+30=0\\\\x^3-2x^2+2x^2-4x-15x+30=0\\\\x^2(x-2)+2x(x-2)-15(x-2)=0\\\\(x-2)(x^2+2x-15)=0\\\\(x-2)(x^2+5x-3x-15)=0\\\\(x-2)(x(x+5)-3(x+5))=0\\\\(x-2)(x+5)(x-3)=0\\\\x-2=0\ \ \ \ \vee\ \ \ \ x+5=0\ \ \ \ \vee\ \ \ \ x-3=0\\\\x=2\ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-5\ \ \ \ \ \ \ \ \vee\ \ \ \ x=3[/tex]
Szczegółowe wyjaśnienie:
1.x3-2x2+3x=0
X*3-2x*2+3x=0
3x-4x+3x=0
2x=0
X=0
2.x(X3+27)(x2-16) (X2+4)=0
X*(x*3+27)*(x*2-16)*(x*2+4)=0
x*(3x+27)*(2x-16)*(2x-4)=0
X=0
3x+27=0
2x-16=0
2x+4=0
X=0
X=-9
X=8
X=-2
X1= - 9
X2=-2
X3=0
X4=8
3. x3-19x+30=0
3x-19x+30=0
16x+3=0
-16x=-30
X=15/8
