+Wyznacz AUB AnB AB BA zbiorów A)(-3:7) B)<-5;3> 2, Podane wyrażenie doporowadz di najprostrzej postaci i oblicz jego wartośc dla x = 1/3. (1+3x)(1-3)+(5x+3)^2-(3-5x)^2

Zadanie 1: [latex]A = (-3;7)[/latex] [latex]B = [-5;3][/latex] [latex]xin(Acup B) Leftrightarrow (xin A lor xin B)[/latex] [latex]Acup B = [-5;7)[/latex] [latex]xin(Acap B) Leftrightarrow (xin A land xin B)[/latex] [latex]Acap B = (-3;3][/latex] [latex]xin (Asetminus B) = (x in A land x otin B)[/latex] [latex]Asetminus B = (3;7)[/latex] [latex]Bsetminus A = [-5;-3][/latex] Zadanie 2: [latex](1 + 3x)(1-3x)+(5x+3)^2-(3-5x)^2 =[/latex] [latex]=1 - 9x^2 + 25x^2 + 30x + 9 - (9 - 30x + 25x^2) =[/latex] [latex]=16x^2+30x+10-9+30x-25x^2=-9x^2+60x+1[/latex] Dla [latex]x = cfrac{1}{3}[/latex] mamy: [latex]-9 cdot left(cfrac{1}{3} ight)^2 + 60 cdot cfrac{1}{3} + 1 = -9 cdot cfrac{1}{9} + 20 + 1 = 20[/latex]