Odpowiedź:
[tex]a)\\\\(4x-20)(x+7)(9-4x)=0\\\\4x-20=0\ \ |:4\ \ \ \ \vee\ \ \ \ x+7=0\ \ \ \ \vee\ \ \ \ 9-4x=0\\\\x-5=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-7\ \ \ \ \ \ \vee\ \ \ \ -4x=-9\ \ |:(-4)\\\\x=5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-7\ \ \ \ \ \ \vee\ \ \ \ x=\frac{9}{4}[/tex]
[tex]b)\\\\x^5+7x^4-8x^3=0\\\\x^3(x^2+7x-8)=0\\\\x^3(x^2+8x-x-8)=0\\\\x^3(x(x+8)-(x+8))=0\\\\x^3(x+8)(x-1)=0\\\\x^3=0\ \ \ \ \vee\ \ \ \ x+8=0\ \ \ \ \vee\ \ \ \ x-1=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=-8\ \ \ \ \ \ \ \ \vee\ \ \ \ x=1[/tex]
[tex]c)\\\\x^3-2x^2-16x+32=0\\\\x^2(x-2)-16(x-2)=0\\\\(x-2)(x^2-16)=0\\\\(x-2)(x-4)(x+4)=0\\\\x-2=0\ \ \ \ \vee\ \ \ \ x-4=0\ \ \ \ \vee\ \ \ \ x+4=0\\\\x=2\ \ \ \ \ \ \ \ \vee\ \ \ \ x=4\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-4[/tex]
[tex]d)\\\\x^4-13x^2+36=0\ \ \ \ \ \ Podstawmy\ \ t=x^2\\\\(x^2)^2-13x^2+36=0\\\\t^2-13t+36=0\\\\t^2-4t-9t+36=0\\\\t(t-4)-9(t-4)=0\\\\(t-4)(t-9)=0\\\\t-4=0\ \ \ \ \vee\ \ \ \ t-9=0\\\\t=4\ \ \ \ \ \ \ \ \vee\ \ \ \ t=9\\\\\\x^2=4\ \ \ \ \vee\ \ \ \ x^2=9\\\\x=\sqrt{4}\ \ \ \ \vee\ \ \ \ x=-\sqrt{4}\ \ \ \ \vee\ \ \ \ x=\sqrt{9}\ \ \ \ \vee\ \ \ \ x=-\sqrt{9}\\\\x=2\ \ \ \ \ \ \vee\ \ \ \ x=-2\ \ \ \ \ \ \vee\ \ \ \ x=3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-3[/tex]
[tex]e)\\\\x^3-7x^2+12x=0\\\\x(x^2-7x+12)=0\\\\x(x^2-3x-4x+12)=0\\\\x(x(x-3)-4(x-3))=0\\\\x(x-3)(x-4)=0\\\\x=0\ \ \ \ \vee\ \ \ \ x-3=0\ \ \ \ \vee\ \ \ \ x-4=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=4[/tex]
