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Question

The number of real solutions of the equation |x|23|x|+2=0 are 

 



Your Answer
A

1

Your Answer
B

2

Your Answer
C

3

Correct Answer
D

4


Solution

The correct option is D

4


Given |x|23|x|+2=0

Here we consider two cases viz.x < 0 and x > 0

Case 1: x < 0 This gives x2+3x+2=0

(x+2)(x+1)=0 ⇒ x=2,1

Also x=1,2  satisfy  x<0, so x=1,2 is solution in this case

Case 2: x > 0. This gives x23x+2=0

⇒ (x-2)(x-1) = 0 ⇒ x =2,1. so, x=2,1 is solution in this case. Hence the number5 of solutions are four i.e. x = -1, -2, 1, 2

Aliter : |x|23|x|+2=0

⇒ (|x|-1)(|x|-2)=0

⇒ |x| = 1 and |x| = 2 ⇒ x = ±1, x = ±2.

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