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Question

The number of real solution(s) of ||x2|2|2|x|=|x3| is

A
1
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B
0
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C
2
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D
3
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Solution

The correct option is B 0
Given : ||x2|2|2|x|=|x3|
The sign of mod changes at 0,2,3

When x<0
|x+22|+2x=x+3|x|=3x+3x=3x+3x=32
No solution.

When 0x2
|x+22|2x=x+3|x|=x+3x=x+30=3
Which is not possible.

When 2<x<3
|x22|2x=x+3|x4|=x+3x+4=x+3x=12
No solution.

When x3
|x22|2x=x3|x4|=3x3
If x4, we get
x4=3x3x=12
No solution.
If x<4, we get
x+4=3x3x=74
No solution as x3

Hence, there is no solution of the given equation.

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