1. [latex]A =(-infty ;0)[/latex] [latex]B=<-1;4>[/latex] [latex]Acap B=<-1; 0)[/latex] [latex]Acup B=(- infty ; 4>[/latex] [latex]A setminus B=(- infty ; -1)[/latex] [latex]B setminus A=<0; 4>[/latex] ---------------- [latex]A=<2;7)[/latex] [latex]B=(3;8>[/latex] [latex]Acap B=(3; 7)[/latex] [latex]Acup B= <2; 8>[/latex] [latex]A setminus B=<2; 3>[/latex] [latex]B setminus A=<7; 8>[/latex] 2. [latex]6x-(4-2x)>2-(6-8x)[/latex] [latex]6x-4+2x>2-6+8x[/latex] [latex]6x+2x-8x>2-6+4[/latex] [latex]0>0[/latex] Nierówność nie ma rozwiązania. [latex]9-(3x-6) ge x+1[/latex] [latex]9-3x+6ge x+1[/latex] [latex]-3x-xge1-9-6[/latex] [latex]-4x ge -14 /:(-4)[/latex] [latex]x ge 3,5[/latex] 3. [latex](2x+1)^2+(x-2)^2=4x^2+4x+1+x^2-4x+4=\ \5x^2+5[/latex] 4. a) [latex]frac{3}{ sqrt{3} }=frac{3sqrt{3}}{ sqrt{3}cdot sqrt{3} }= frac{3sqrt{3}}{3} =sqrt{3}[/latex] b) [latex]frac{4}{ sqrt{6}-2}= frac{4(sqrt{6}+2)}{(sqrt{6}-2)(sqrt{6}+2)} = frac{4(sqrt{6}+2)}{6-4}=[/latex] [latex]frac{4(sqrt{6}+2)}{2}=2(sqrt{6}+2)[/latex]
