If - x 2-2 x -3- x -3- x 2- x - then x lies inA- -3-0- -3- -B- -3- - -3-1- -3- -D- -3-1- -3- -

The correct option is C [ 3, 1]∪[3,∞)|x^2 2x 3|+|x+3|=|x^2 x| nbsp; Let x^2 2x 3=a, x+3=b Here a+b=x^2 x Clearly, |a|+|b|=|a+b| that is possible only when a ...

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Byju's Answer

Standard XII

Mathematics

Absolute Value Function

If | x 2-2 x ...

Question

If $| x^{2} - 2 x - 3 | + | x + 3 | = | x^{2} - x |$ , then $x$ lies in

[3, \infty)

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[- 3, 0] \cup [3, \infty)

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[- 3, - 1] \cup [3, \infty)

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[- 3, 1] \cup [3, \infty)

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Solution

The correct option is C $[- 3, - 1] \cup [3, \infty)$
$| x^{2} - 2 x - 3 | + | x + 3 | = | x^{2} - x |$
Let $x^{2} - 2 x - 3 = a, x + 3 = b$
Here $a + b = x^{2} - x$
Clearly, $| a | + | b | = | a + b |$ that is possible only when
$a b \geq 0$
$\Rightarrow (x^{2} - 2 x - 3) (x + 3) \geq 0$
$\Rightarrow (x - 3) (x + 1) (x + 3) \geq 0$
$\Rightarrow x \in [- 3, - 1] \cup [3, \infty)$

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If |x2−2x−3|+|x+3|=|x2−x|, then x lies in

The correct option is C [−3,−1]∪[3,∞)|x2−2x−3|+|x+3|=|x2−x| Let x2−2x−3=a, x+3=b Here a+b=x2−x Clearly, |a|+|b|=|a+b| that is possible only when ab≥0 ⇒(x2−2x−3)(x+3)≥0 ⇒(x−3)(x+1)(x+3)≥0 ⇒x∈[−3,−1]∪[3,∞)

If $| x^{2} - 2 x - 3 | + | x + 3 | = | x^{2} - x |$ , then $x$ lies in