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Math Help - sqrt(2)-1 = 1/(sqrt(2)+1)

  1. #1
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    sqrt(2)-1 = 1/(sqrt(2)+1)

    sqrt(2)-1 = 1/(sqrt(2)+1)

    Can someone show me how this is possible?
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  2. #2
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    Quote Originally Posted by techmath View Post
    sqrt(2)-1 = 1/(sqrt(2)+1)

    Can someone show me how this is possible?
    Multiply by the conjugate:
    (\sqrt{2}-1)  \cdot \frac{\sqrt{2}+1}{\sqrt{2}+1} = \ldots
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  3. #3
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    Quote Originally Posted by techmath View Post
    sqrt(2)-1 = 1/(sqrt(2)+1)

    Can someone show me how this is possible?
    Multiply through by \sqrt2 + 1

    (\sqrt2 -1)(\sqrt2 +1) = 1

    Note that the left hand side is the difference of two squares
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by techmath View Post
    sqrt(2)-1 = 1/(sqrt(2)+1)

    Can someone show me how this is possible?
    Note that \sqrt{2}-1=\left(\sqrt{2}-1\right)\cdot1=\left(\sqrt{2}-1\right)\frac{\sqrt{2}+1}{\sqrt{2}+1}=\frac{\left(  \sqrt{2}-1\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=\frac  {2-1}{\sqrt{2}+1} =\frac{1}{\sqrt{2}+1}

    Does this make sense?

    EDIT: Grr...I'm too slow today... XD
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