Answer to Question #12716 in Real Analysis for DivyaGoel

Question

Find all real numbers x that satisfy the following inequalities.
1<x2<4

Answer 1

1<x^2<4 it mean that x^2>1 and x^2<4
x^2<4 so
-2<x<2
x^2>1 so x<-1 or x>1
then the common solution
(-2<x<2) and (x<-1 or x>1)
then -2<x<-1 or 1<x<2