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Question

# Consider ∣∣x−2eln3∣∣+∣∣x+2eln3∣∣=12. Then which of the following statement(s) is(are) CORRECT ?

A
The number of integral solutions of the equation is 7.
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B
The number of integral solutions of the equation is 13.
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C
The sum of all the integral solutions of the equation is 0.
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D
The sum of all the integral solutions of the equation is 28.
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Solution

## The correct option is C The sum of all the integral solutions of the equation is 0.|x−2eln3|+|x+2eln3|=12 ⇒|x−6|+|x+6|=12 Case−1:x<−6 −x+6−x−6=12 ⇒x=−6 ( rejected ) Case−2:−6≤x≤6 −x+6+x+6=12 12=12 ∴x∈[−6,6] Case−3:x>6 x−6+x+6=12 ⇒x=6 ( rejected ) ∴x∈[−6,6] ∴ Number of integral solutions is 13,{−6,−5,...,5,6} and sum of these integral solutions is zero.

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