1.Rozwiąż równanie kwadratowe x kwadrat + x - 20 = 0 , 2.Podaj rozwiązanie nierówności (x+3)(x-1)>0 ,

1. [latex]x^2+x-20=0 \ (x^2+x+frac{1}{4})-20-frac{1}{4}=0 \ (x+frac{1}{2})^2-20frac{1}{4}=0 \ (x+frac{1}{2})^2=20frac{1}{4} \ (x+frac{1}{2})^2=frac{81}{4} \ sqrt{(x+frac{1}{2})^2}=sqrt{frac{81}{4}} \ |x+frac{1}{2}|=frac{9}{2} \ x+frac{1}{2}=-frac{9}{2} lor x+frac{1}{2}=frac{9}{2} \ x=-frac{9}{2}-frac{1}{2} lor x=frac{9}{2}-frac{1}{2} \ x=-frac{10}{2} lor x=frac{8}{2} \ x=-5 lor x=4 \ x in {-5, 4}[/latex] 2. [latex](x+3)(x-1)>0 \ \ dla x>1 \ (x+3)(x-1)>0 \ x+3>0 \ x>-3 \ x>1 \ \ dla x<1 \ (x+3)(x-1)>0 \ x+3<0 \ x<-3 \ x<-3 \ \ x in (-infty,-3) cup (1,+infty)[/latex]

1) [latex] x^{2} + x - 20 = 0 [/latex] Δ = [latex] 1^2 - 4*1*(-20) = 1 + 80 = 81[/latex] √Δ = 9 [latex]x_1 = frac{-1 + 9}{2} = frac {8} {2} = 4 \ x_2 = frac{-1 - 9}{2} = frac{-10}{2} = -5 [/latex] 2) (x+3)(x-1) > 0 x+3 > 0       x-1>0 x > -3          x>1