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  4. The number of elements in the set x ∈ R :(|x|-3)|x+4|=6 is equal to

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Q. The number of elements in the set $\{x \in R :(|x|-3)|x+4|=6\}$ is equal to

JEE MainJEE Main 2021Complex Numbers and Quadratic Equations

Solution:

$x \neq-\,4$
$(|x|-3)(|x+4|)=6$
$\Rightarrow \quad|x|-3=\frac{6}{|x+4|}$
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No. of solutions $= 2$