[tex]zad.1\\a)\\x(x^{3} -1)(3x-5)(2x^{3} +3)=0\\\\x=0~~\lor x^{3}-1=0 ~~\lor ~~3x-5=0~~\lor ~~2x^{3} +3=0\\\\x=0~~\lor x^{3}=1 ~~\lor ~~3x=5~~\lor ~~2x^{3}=-3\\\\x=0~~\lor~~ x=1~~\lor~~x=\frac{5}{3} ~~\lor~~x^{3} =-\frac{3}{2}\\\\x=0~~\lor~~ x=1~~\lor~~x=\frac{5}{3} ~~\lor~~x=\sqrt[3]{(-\frac{3}{2} } )\\b)\\2x^{2} (x^{2} -3)(x^{2} -4x+4)=0\\\\2x^{2} (x^{2} -3)(x-2)^{2}=0\\\\2x^{2} =0~~\lor~~x^{2} -3=0~~\lor~~x-2=0\\\\x=0~~\lor~~ (x-\sqrt{3} )(x+\sqrt{3} )=0~~\lor x=2[/tex]
[tex]x=0~~\lor ~~x=\sqrt{3} ~~~\lor~~x=-\sqrt{3} ~~\lor~~ x= 2[/tex]
[tex]zad.2\\a)\\x^{3} -3x^{2} =4x-12\\\\x^{2} (x-3)=4(x-3)\\\\x^{2} (x-3)-4(x-3)=0\\\\(x-3)(x^{2} -4)=0\\\\(x-3)(x+2)(x-2)=0\\\\x-3=0~~\lor~~ x+2=0~~\lor~~x-2=0\\\\x=3~~\lor~~ x=-2~~\lor~~x=2\\b)\\x^{3} -5x^{2} =-10+2x\\\\x^{2} (x-5)=2x-10\\\\x^{2} (x-5)=2(x-5)\\\\x^{2} (x-5)-2(x-5)=0\\\\(x-5)(x^{2} -2)=0\\\\(x-5)(x-\sqrt{2} )(x+\sqrt{2})=0\\\\x-5=0~~\lor~~x-\sqrt{2} =0~~\lor~~x+\sqrt{2} =0\\\\x=5~~\lor~~ x=\sqrt{2}~~\lor~~x=-\sqrt{2}[/tex]
