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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.$\left|x^2-x-6\right|=x+2$
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Answer

$\left|x^2-x-6\right|=x+2 \ldots$.(i)
R.H.S. must be non-negative
$ \therefore x \geq-2 \ldots \text {.(ii) }$
$|(x-3)(x+2)|=x+2$
$\therefore(x+2)|x-3|=x+2 \text { as } x+2 \geq 0$
$\therefore|x-3|=1 \text { if } x \neq-2$
$\therefore x-3= \pm 1$
$\therefore x=4 \text { or } 2 $
$\therefore \mathrm{x}=-2$ also satisfies the equation
$\therefore$ Solution set $=\{-2,2,4\}$

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