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Thread: pls tell me how to do this :(

  1. #1
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    please tell me how to do this :(

    express (2+sqrt3)(5-2sqrt3) in the form a+bsqrtc.

    the answer is 4+sqrt3.
    can someone teach me how to get it ?
    Last edited by charl0tte; Jun 3rd 2006 at 09:35 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by charl0tte
    express (2+sqrt3)(5-2sqrt3) in the form a+bsqrtc.

    the answer is 4+sqrt3.
    can someone teach me how to get it ?
    To express $\displaystyle (2+\sqrt 3)(5-2\sqrt 3)$ in the form $\displaystyle a+b\sqrt c$ begin by multiplying out the brackets:

    $\displaystyle
    (2+\sqrt 3)(5-2\sqrt 3)=2(5-2\sqrt 3)+\sqrt 3 (5-2\sqrt 3)
    $
    $\displaystyle
    =10-4\sqrt 3 + \sqrt 3 (5-2\sqrt 3)
    $

    $\displaystyle
    =10-4\sqrt 3 + 5\sqrt 3-2\sqrt 3 \sqrt 3
    $

    $\displaystyle
    =10-4\sqrt 3 + 5\sqrt 3-6
    $

    $\displaystyle
    =4+\sqrt 3
    $

    RonL
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  3. #3
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    thx !!
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