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Question

The number of solutions of the equation 9x218|x|+5=0 belonging to the domain of definition of loge{(x+1)(x+2)}, is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 3

f(x)=loge{(x+1)(x+2)}

For the function to be defined

(x+1)(x+2)>02>x>1x(,2)(1,)

9x218|x|+5=09|x|218|x|+5=09|x|218|x|+5=0for(x>0)9|x|23|x|15|x|+5=03|x|(3|x|1)5(3|x|1)=0(3|x|1)(3|x|5)=0|x|=13,53x=13,53,13,53

Clearly 53 do not belong to the domain of the function f(x)

So there are 3 solutions belonging to the domain of f(x)

Option C is ccorrect.


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