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Math Help - Basic Arithmetic and Surds

  1. #1
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    Basic Arithmetic and Surds

    Express (2root5 - 3root10)^2 in the form a+broot2 and hence find the values of a and b. If you can please help and explain the method and how to solve equations similar to this. Thanks
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  2. #2
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    Re: Basic Arithmetic and Surds

    That is not an equation. Anyway:

    (a-b)^2=a^2-2ab+b^2, so:

    (2\sqrt 5-3\sqrt {10})^2=(2\sqrt 5)^2-2\cdot 2\sqrt 5 \cdot 3\sqrt {10} + (3\sqrt {10})^2=

    =4\cdot 5-12\sqrt{5\cdot 10}+3\cdot 10=20-12\cdot 5 \sqrt 2 +30=50-60\sqrt 2

    a = 50, b = -60
    Last edited by veileen; March 6th 2013 at 09:50 PM.
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  3. #3
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    Re: Basic Arithmetic and Surds

    Alice

    show us some of your work...apply the well known identity (a-b)^2 =a^2+b^2-2ab....where a and b could be anything...in your case 2root5 or 2root10......try it
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