Equations And Inequalities Question 37
Question: The number of real roots of the equation $ | 2-| 1-| x | | |=1 $ is
Options:
A) 1
B) 3
C) 5
D) 6
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ | 2-| 1-| x | | |=1\Rightarrow 2-| 1-| x | |=\pm 1 $
$ \Rightarrow | 1-| x | |=1or3 $ If $ | | 1- |x |=1\Rightarrow 1-| x |=\pm 1\Rightarrow | x |=0or2 $
$ \Rightarrow x=0or\pm 2 $ If $ | 1-| x | |=3\Rightarrow 1-| x |=\pm 3\Rightarrow | x |=-2or4 $
$ \Rightarrow | x |=4\Rightarrow x=\pm 4 $ $ [\because | x |\ne -2] $
$ \therefore $ Solution set is $ {-4,-2,0,2,4} $ , hence 5 real roots in all.
BETA
