1. ## absolute value notation

hello, I'm confused about the solution to this expression for x<0 :

sqrt(-x|x|)=

I know that for x<0 I get sqrt(x^2)
but then to me both x and -x are solutions.

could you explain what I'm doing wrong so I won't make the same mistake?

thank you!

2. Originally Posted by simone
hello, I'm confused about the solution to this expression for x<0 :

sqrt(-x|x|)=

I know that for x<0 I get sqrt(x^2)
but then to me both x and -x are solutions.

could you explain what I'm doing wrong so I won't make the same mistake?

thank you!
By definition:
$|x|=\left\{\begin{array}{rr}x,\text{ if }x>0\\
-x,\text{ if }x<0\\
0,\text{ if }x=0\end{array}\right.$

So when x is negative (or 0):
$\sqrt{-x|x|} = \sqrt{-x \cdot -x} = \sqrt{x^2} = |x|$

When x is positive:
$\sqrt{-x|x|} = \sqrt{-x \cdot x} = \sqrt{-x^2}$
which is undefined (or an imaginary number, depending on what you are working on.)

-Dan