Odpowiedź:
[tex]a)\\\\x^3+3x^2-9x=27\\\\x^3+3x^2-9x-27=0\\\\x^2(x+3)-9(x+3)=0\\\\(x+3)(x^2-9)=0\\\\(x+3)(x-3)(x+3)=0\\\\(x+3)^2(x-3)=0\\\\(x+3)^2=0\ \ \ \ \vee\ \ \ \ x-3=0\\\\x+3=0\ \ \ \ \ \ \vee\ \ \ \ x=3\\\\x=-3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=3\\\\\\b)\\\\2x^3+8x=5x^2+20\\\\2x(x^2+4)=5(x^2+4)\\\\2x(x^2+4)-5(x^2+4)=0\\\\(x^2+4)(2x-5)=0\\\\x^2+4=0\ \ \ \ \vee\ \ \ \ 2x-5=0\\\\x^2=-4\ \ brak rozwiazania\\\\\\2x-5=0\\\\2x=5\ \ /:2\\\\x=\frac{5}{2}[/tex]
[tex]c)\\\\x^5+x^2=8x^3+8\\\\x^2(x^3+1)=8(x^3+1)\\\\x^2(x^3+1)-8(x^3+1)=0\\\\(x^3+1)(x^2-8)=0\\\\(x+1)(x^2-x+1)(x^2-8)=0\\\\x+1=0\ \ \ \ \vee\ \ \ \ x^2-x+1=0\ \ \ \ \vee\ \ \ \ x^2-8=0\\\\x=-1\\\\\\x^2-x+1=0\\\\a=1\ \ ,\ \ b=-1\ \ ,\ \ c=1\\\\\Delta=b^2-4ac\\\\\Delta=(-1)^2-4\cdot1\cdot1=1-4=-3\\\\\Delta<0\ \ brak\ \ rozwiazania\\\\\\x^2-8=0\\\\x^2=8\\\\x=\sqrt{8}\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-\sqrt{8}\\\\x=\sqrt{4\cdot2}\ \ \ \ \vee\ \ \ \ x=-\sqrt{4\cdot2}[/tex]
[tex]x=2\sqrt{2}\ \ \ \ \ \ \vee\ \ \ \ x=-2\sqrt{2}\\\\R\'ownanie\ \ ma\ \ 3\ \ rozwiazania\\\\x=-2\sqrt{2}\ \ \ \ \vee\ \ x=-1\ \ \ \ \vee\ \ \ \ x=2\sqrt{2}[/tex]
