x^2-2(m+3)x+m^2-1=0
-
\Delta>0
-
x_1+x_2<0
-
x_1*x^2>0
-
x^2-2(m+3)x+m^2-1>0
a=1, b=-2(m+3), c=m^2-1
b^2-4ac>0
[-2(m+3)]^2-4(m^2-1)>0
4(m^2+6m+9)-4m^2+4>0|:4
m^2+6m+9-m^2+1>0
6m+10>0
6m>-10
m>-\frac{10}{6}
m>-\frac{5}{3}
m>-1\frac{2}{3}
m\in(-1\frac{2}{3};+\infty) (1)
-
x_1+x_2<0
-\frac{b}{a}<0
\frac{-[-2(m+3)]}{1}<0
2m+6<0
2m<-6
m<-3
m<-1\frac{1}{2}
x\in (-\infty;-1\frac{1}{2}) (2)
-
x_1*x_1>0
\frac{c}{a}>0
\frac{m^2-1}{1}>0
m^2-1>0
(m-1)(m+1)>0
m-1 m=-1
m\in (-1;1) (3)
część wspólna (1), (2), (3)
m\in\emptyset zbiór pusty