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Absolute Value Function

If |x + 3| = ...

Question

If $| x + 3 | = x^{2} - 4 x - 3$ , then $x =$

A

0

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B

3

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C

6

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D

1

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Solution

The correct option is C $6$
When $x < - 3$
$- x - 3 = x^{2} - 4 x - 3 \Rightarrow x^{2} - 3 x = 0$
$\Rightarrow x (x - 3) = 0$
$\Rightarrow x = 0, 3 (Not possible)$

When $x \geq - 3$
$x + 3 = x^{2} - 4 x - 3$
$\Rightarrow x^{2} - 5 x - 6 = 0$
$\Rightarrow (x - 6) (x + 1) = 0 \Rightarrow x = 6, - 1$

$∴ x = - 1, 6$

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