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Question

If ||x3|4|=3, then there exist


A
exactly 2 distinct values of x in [1,5]
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B
exactly 2 distinct values of x in [5,0] 
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C
exactly 2 distinct values of x in [1,10] 
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D
exactly 4 distinct values of x in [5,10] 
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Solution

The correct options are
A exactly 2 distinct values of x in [1,5]
D exactly 4 distinct values of x in [5,10] 
Case 1:|x3|40 i.e., x(,1][7,) 
Then |x3|4=3
|x3|=7
x=10 or x=4
x=4,10     (1)

Case 2:|x3|4<0 i.e., x(1,7) 
Then |x3|4=3
|x3|=1
x=2,4     (2)

Hence, from (1) and (2), x=4,2,4,10

Mathematics

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