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Math Help - absolute value notation

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by simone View Post
    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\\<br />
-x,\text{ if }x<0\\<br />
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
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