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Math Help - Prove equality

  1. #1
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    [RESOLVED]Prove equality

    a and b are real numbers.

    demonstrate the following equality.
    |ab|=|a||b|



    I have no idea, how to prove that.

    I just know |a+b|\leq|a|+|b| so i dont know how to start.
    Last edited by Fabio010; October 17th 2011 at 10:55 AM.
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  2. #2
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    Re: Prove equality

    Quote Originally Posted by Fabio010 View Post
    a and b are real numbers. demonstrate the following equality.
    |ab|=|a||b|
    Just bite the bullet.
    There are four cases:
    \begin{gathered}  a \geqslant 0\;\& \,b \geqslant 0 \hfill \\  a \geqslant 0\;\& \,b < 0 \hfill \\  a < 0\;\& \,b \geqslant 0 \hfill \\  a < 0\;\& \,b < 0 \hfill \\ \end{gathered}

    Take the last case:
    (-a)(-b)=ab>0 so ab=|ab|.
    But -a=|a|~\&~-b=|b| so |a||b|=|ab|
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  3. #3
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    Re: Prove equality

    Quote Originally Posted by Plato View Post
    Just bite the bullet.
    There are four cases:
    \begin{gathered}  a \geqslant 0\;\& \,b \geqslant 0 \hfill \\  a \geqslant 0\;\& \,b < 0 \hfill \\  a < 0\;\& \,b \geqslant 0 \hfill \\  a < 0\;\& \,b < 0 \hfill \\ \end{gathered}

    Take the last case:
    (-a)(-b)=ab>0 so ab=|ab|.
    But -a=|a|~\&~-b=|b| so |a||b|=|ab|
    OK thanks a lot for the help
    but

    even if ab<0 isnt ab= |ab| ??
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  4. #4
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    Re: Prove equality

    Quote Originally Posted by Fabio010 View Post
    OK thanks a lot for the help
    but even if ab<0 isnt ab= |ab| ??
    No one said it was. Nowhere was that ever even mentioned.
    This is true: If ab<0 then -ab=|ab|
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  5. #5
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    Re: Prove equality

    ok

    so i can prove with all cases :/???
    because if -ab = |ab|
    -a = |a|~\&~b = |b|~so |a||b| = |ab|

    sorry if i am being confusing.
    Last edited by Fabio010; October 17th 2011 at 09:40 AM.
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  6. #6
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    Re: Prove equality

    ??can i prove with all cases?
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  7. #7
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    Re: Prove equality

    Quote Originally Posted by Fabio010 View Post
    ??can i prove with all cases?
    What does that mean?
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  8. #8
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    Re: Prove equality

    Sorry i was confusing.
    Now i understood it completely.

    Thanks for the help.
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