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Proof of an expression involving absolute value

  1. Dec 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove: |ab|=|a||b|. (Hint: Consider the cases separately for various signs of a and b.)

    2. Relevant equations

    I think it asks me to prove it only from the definition of absolute value (if it is possible).

    3. The attempt at a solution

    |ab|= [itex]\frac{(ab), if (ab)\geq0}{-(ab), if (ab)<0}[/itex]

    I do the same with |a||b| .... but does it constitute a proof?

    I actually have no idea how to prove such a thing.
     
    Last edited: Dec 17, 2011
  2. jcsd
  3. Dec 17, 2011 #2
    Sry for the interruption, i found the answers in this forum ...
     
  4. Dec 17, 2011 #3
    Could you say this:

    abs(ab) = positive sqrt((ab)^2) = positive sqrt((a^2)(b^2)) = positive sqrt(a^2)*positive sqrt(b^2) = abs(a)*abs(b)
     
  5. Dec 17, 2011 #4
    So you've got the problem solved or do you need more into it?
     
  6. Dec 17, 2011 #5
    Yeah I found the proof in the other threads
     
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