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Math Help - Show: |x|^2=x^2

  1. #1
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    Show: |x|^2=x^2

    Is the following argument valid?

    1. |x| = {x, if x>0; -x, if x<0}; True statement
    2. We check both cases:
    For x>0, |x|^2= (|x|)^2 = (x)^2 = x^2
    For x<0, |x|^2= (|x|)^2 = (-x)^2 = [(-1)^2][(x)^2] = x^2
    Thus, |x|^2 and x^2 are interchangeable expressions.
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  2. #2
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    Re: Show: |x|^2=x^2

    Quote Originally Posted by Elusive1324 View Post
    Is the following argument valid?

    1. |x| = {x, if x>0; -x, if x<0}; True statement
    2. We check both cases:
    For x>0, |x|^2= (|x|)^2 = (x)^2 = x^2
    For x<0, |x|^2= (|x|)^2 = (-x)^2 = [(-1)^2][(x)^2] = x^2
    Thus, |x|^2 and x^2 are interchangeable expressions.
    What happens when x=0?

    .
    Thanks from topsquark
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