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Math Help - Quick Reciprocal Problem

  1. #1
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    Quick Reciprocal Problem

    Hello All,

    I wanted to ask if someone could enlighten me with the reciprocal of 2+5*Sqrt(3).

    I've just inverted all of it and I multiplied it by the conjugate, but i'm not sure if thats the right way to head with this thing.

    Any help is appreciated!
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  2. #2
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    Quote Originally Posted by Samson View Post
    Hello All,

    I wanted to ask if someone could enlighten me with the reciprocal of 2+5*Sqrt(3).

    I've just inverted all of it and I multiplied it by the conjugate, but i'm not sure if thats the right way to head with this thing.

    Any help is appreciated!
    Dear Samson,

    The reciprocal of 2+5\sqrt{3} is \frac{1}{2+5\sqrt{3}}. You could multiply the numerator and denominator by the conjugate if you want to,

    \frac{1}{2+5\sqrt{3}}=\frac{1}{2+5\sqrt{3}}\times\  frac{2-5\sqrt{3}}{2-5\sqrt{3}}=-\frac{2-5\sqrt{3}}{71}

    Hope this will help you.
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  3. #3
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    Quote Originally Posted by Sudharaka View Post
    Dear Samson,

    The reciprocal of 2+5\sqrt{3} is \frac{1}{2+5\sqrt{3}}. You could multiply the numerator and denominator by the conjugate if you want to,

    \frac{1}{2+5\sqrt{3}}=\frac{1}{2+5\sqrt{3}}\times\  frac{2-5\sqrt{3}}{2-5\sqrt{3}}=-\frac{2-5\sqrt{3}}{71}

    Hope this will help you.
    That is what I was saying I needed to do, however I'm not sure if you still have that -71 in the denominator if that counts as still being in the form of a+b*Sqrt(3) . (For what is worth I got the same thing but i'm not sure if its right when I'm supposed to be able to put it into a form like that).
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  4. #4
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    Quote Originally Posted by Samson View Post
    That is what I was saying I needed to do, however I'm not sure if you still have that -71 in the denominator if that counts as still being in the form of a+b*Sqrt(3) . (For what is worth I got the same thing but i'm not sure if its right when I'm supposed to be able to put it into a form like that).
    Dear Samson,

    Yes. This is in the a+b\sqrt{3} form, since -\frac{2-5\sqrt{3}}{71}=-\frac{2}{71}+\frac{5}{71}\sqrt{3}
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  5. #5
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    Quote Originally Posted by Sudharaka View Post
    Dear Samson,

    Yes. This is in the a+b\sqrt{3} form, since -\frac{2-5\sqrt{3}}{71}=-\frac{2}{71}+\frac{5}{71}\sqrt{3}
    Okay, so when the book mentions that form its okay that the numbers a and b are not integers?
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  6. #6
    MHF Contributor chiph588@'s Avatar
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    It depends on what ring you're in.
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