Question

1. Find the solution set
​

Answer 1

Answer:

given ∣x+

x

1

∣>2

⇒∣

x

x

2

+1

∣>2

∣x∣

∣x

2

+1∣

=

∣x∣

x

2

+1

>2

⇒x

2

+1>2∣x∣

⇒x

2

−2∣x∣+1>0

if x>0 then (x−1)

2

>0 it is possible for all x

therefore the solution is x>0

if x<0 then (x+1)

2

>0 it is also possible for all x

therefore the solution set is x<0

therefore the overall solution set is x∈R−1