[tex]zad.1\\3x^{2} >8x+3\\\\3x^{2} -8x-3>0\\a=3,~~b=-8,~~c=-3\\\\\Delta=b^{2} -4ac\\\Delta=(-8)^{2} -4\cdot 3\cdot (-3)=64+36=100\\\sqrt{\Delta} =\sqrt{100} =10\\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor ~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a} \\\\x_{1} =\dfrac{8-10}{6} =-\dfrac{1}{3} ~~\lor~~x_{2} =\dfrac{8+10}{6} =3\\\\a=3~~\Rightarrow ~~a>0 ~~-ramiona~~paraboli~~skierowane ~~do ~~gory\\\\x\in (-\infty , -\frac{1}{3} )\cup (3,+\infty )[/tex]
[tex]zad.2\\\\2x^{3} -18x=0\\\\2x\cdot (x^{2} -9)=0~~\mid \div 2\\\\x\cdot (x^{2} -3^{2} )=0\\\\x\cdot (x-3)\cdot (x+3)=0\\\\x=0~~\lor~~x-3=0~~\lor ~~x+3=0\\\\x=0~~\lor ~~x=3~~\lor x=-3\\\\x\in \{ ~~-3,~~0,~~3~~ \}[/tex]
korzystałam ze wzoru skróconego mnożenia: x²- y² = ( x - y ) × ( x + y )
