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Absolute Value Function

If x2-|x+3|+x...

Question

If $x^{2} - | x + 3 | + x = 0$ , then $x =$

A

- \sqrt{3}

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B

\sqrt{3}

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C

3

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D

0

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Solution

The correct options are
A $- \sqrt{3}$
B $\sqrt{3}$
$x^{2} - | x + 3 | + x = 0$
If $x \geq - 3$ ,
then $x^{2} - 3 = 0$
$\Rightarrow x = \sqrt{3}$ or $x = - \sqrt{3}$

If $x < - 3$ ,
then $x^{2} + x + 3 + x = 0$
$\Rightarrow x^{2} + 2 x + 3 = 0$
As $D < 0$ , hence no solution.

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