Rozwiąż równania i nierówności.Zbiór rozwiązań nierówności zaznacz na osi liczbowej. b) x^3=25x c) x^2(x+2)=2(x+2) d) (3x^2-5x+2)(3-2x)^2(9-x)<0 e) 3x^3+5x^2-27x-45

[latex]a)\ \x^3=25x\ \x^3-25x=0\ \x(x^2-25)=0\ \x(x-5)(x+5)=0\ \x=0vee x-5=0vee x+5=0\ \x=0veex=5 vee x=-5[/latex] [latex]c)\ \x^2(x+2)=2(x+2)\ \x^2(x+2)-2(x+2)=0\ \(x+2)(x^2-2)=0\ \(x+2)(x-sqrt{2})(x+sqrt{2})=0\ \x=0vee x=sqrt{2}vee x=-sqrt{2}[/latex] [latex]d)\(3x^2-5x+2)(3-2x)^2(9-x)<0[/latex] miejsca zerowe: [latex]d)\\(3x^2-5x+2)(3-2x)^2(9-x)<0\ \3x^2-5x+2=0\ \Delta = b^{2}-4ac = (-5)^{2}-4*3*2=25-24=1 \ \sqrt{Delta }=sqrt{1}=1\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{5-1}{6}=frac{4}{6}=frac{2}{3}[/latex] [latex]x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{5+1}{6}=frac{6}{6}=1[/latex] [latex]3-2x =0\ \2x=3/:2\ \x=frac{3}{2}[/latex] [latex]9-x =0\ \x=9[/latex] [latex]x=frac{2}{3}wedge x=1wedgex=frac{3}{2} wedge x=9\ \xin(-infty ,frac{2}{3})cup (1,frac{3}{2})cup (9,+infty )[/latex] [latex]e)\ 3x^3+5x^2-27x-45leq 0\ \x^2(3x+5)-9(3x+5)leq 0\ \(3x+5)(x^2-9)leq 0\ \(3x+5)(x-3)(x+3)leq 0[/latex] [latex]3x+5=0wedge x-3=0wedge x+3=0\ \3x=-5wedge x=3wedge x=-3\ \x=-frac{5}{3}wedge x=3wedge x=-3\ \xin(-infty ,-3>cup <-frac{5}{3},3>[/latex]