4.
[tex]4x>x^{2}+4\\\\-x^{2}+4x-4 > 0\\\\M. \ zerowe:\\\\-x^{2}+4x-4 = 0 \ \ /\cdot(-1)\\\\x^{2}-4x+4 = 0\\\\(x-2)^{2} = 0\\\\x-2 = 0\\\\x = 2\\\\x \in \phi[/tex]
5.
[tex]2(x+1)^{2}-(x-3)^{2}\geq 11x-1\\\\2(x^{2}+2x+1) -(x^{2}-6x+9)\geq 11x-1\\\\2x^{2}+4x+2-x^{2}+6x-9\geq 11x-1\\\\x^{2}+10x-7-11x+1 \geq 0\\\\x^{2}-x-6\geq 0\\\\a = 1, \ b = -1, \ c = -6\\\\\Delta = b^{2}-4ac = (-1)^{2}-4\cdot1\cdot(-6) = 1+24 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5[/tex]
[tex]x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-1)-5}{2\cdot1} = \frac{1-5}{2} = \frac{-4}{2} = -2\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-(-1)+5}{2} = \frac{6}{2} = 3[/tex]
a > 0, to ramiona paraboli skierowane do góry
[tex]x\in(-\infty;-2> \ \cup \ <3;+\infty)[/tex]
6.
[tex](x+3)(3-x)>3(x-2)^{2}+5\\\\(3+x)(3-x) >3(x^{2}-4x+4)+5\\\\9-x^{2}>3x^{2}-12x+12+5\\\\-x^{2}+9>3x^{2}-12x+17\\\\-x^{2}-3x^{2}+12x+9-17 > 0\\\\-4x^{2}+12x-8 > 0 \ \ /:(-4)\\\\x^{2}-3x+2<0\\\\a = 1, \ b = -3, \ c = 2\\\\\Delta = b^{2}-4ac = (-3)^{2}-4\cdot1\cdot2 = 9-8 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1 = \frac{-(-3)-1}{2} = \frac{2}{2} = 1\\\\x_2 = \frac{-(-3)+1}{2} = \frac{4}{2} = 2\\\\a =1 > 0\\\\x \in (1;2)[/tex]
