1.
[tex]x^{2}-3(x-3) < 9-3x\\\\x^{2}-3x+9 -9+3x < 0\\\\x^{2} < 0, \ sprzecznosc\\\\a > 0, \ ramiona \ paraboli \ skierowane \ do \ gory\\\\x \in \phi[/tex]
2.
[tex]x - 6x^{2} < 0\\\\-6x^{2} +x < 0\\\\M. \ zerowe:\\\\x(-6x+1) =0\\\\x = 0 \ \vee \ -6x+1 = 0\\\\x = 0 \ \vee \ -6x = -1 \ \ /:(-6)\\\\x = 0 \ \vee x = \frac{1}{6}\\\\a < 0, \ to \ ramiona \ paraboli \ skierowane \ do \ dolu, \ wowczas\\\\\boxed{x \in (-\infty;0) \ \cup \ (\frac{1}{6}; +\infty)}[/tex]
3.
[tex]2x^{2}+1 > 0\\\\a = 2, \ b = 0, \ c = 1\\\\\Delta = b^{2}-4ac = 0^{2}-4\cdot2\cdot1 = -8 \ < 0\\\\Wykres \ paraboli \ nie \ przecina \ osi \ Ox, \ zatem\\\\\boxed{x \in R}[/tex]
