If -x-3-x-1-12- then x-A- -3B- 5C- 3D- -5

The correct options are A 3 nbsp; B 5 nbsp;|x − 3||x + 1| =12 ⇒|x^2 − 2x − 3| = 12 Case 1: x^2 − 2x − 3 ≥ 0 i.e., x∈( ∞, 1]∪ [3,∞) Then x^2 − 2x − 3 = 12 ...

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Byju's Answer

Standard XII

Mathematics

Absolute Value Function

If |x-3||x+1|...

Question

If $| x - 3 | | x + 1 | = 12,$ then $x =$

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Solution

The correct options are
A $- 3$
B $5$
$| x - 3 | | x + 1 | = 12$
$\Rightarrow | x^{2} - 2 x - 3 | = 12$

$Case 1 : x^{2} - 2 x - 3 \geq 0 i.e., x \in (- \infty, - 1] \cup [3, \infty)$
Then $x^{2} - 2 x - 3 = 12$
$\Rightarrow x^{2} - 2 x - 15 = 0$
$\Rightarrow (x - 5) (x + 3) = 0$
$\Rightarrow x = - 3, 5$

$Case 2 : x^{2} - 2 x - 3 < 0 i.e., x \in (- 1, 3)$
Then $x^{2} - 2 x - 3 = - 12$
$\Rightarrow x^{2} - 2 x + 9 = 0$
$\Rightarrow (x - 1)^{2} + 8 = 0$ (Not possible)

Suggest Corrections

If |x−3||x+1|=12, then x=

If $| x - 3 | | x + 1 | = 12,$ then $x =$