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Math Help - Continued root of 2

  1. #1
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    Continued root of 2

    Hey guys,

    I'm having trouble with this question here.

    Continued root of 2-capture.png

    I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

    p.s. the question gives a hint saying "Find X^2 in terms of X"

    Thanks ^_^
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  2. #2
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    Quote Originally Posted by DrizzlyDays View Post
    Hey guys,

    I'm having trouble with this question here.

    Click image for larger version. 

Name:	Capture.PNG 
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ID:	18036

    I have to find the value of the continued root of 2 (shown in image) algebraically. Could someone please walk me through it?

    p.s. the question gives a hint saying "Find X^2 in terms of X"

    Thanks ^_^
    First note that X can't be negative, because of the definition of \sqrt{}. Then square both sides. What do you see?
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  3. #3
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    Well, wouldn't it be:

    X^2 = 2 + *continued root*?

    or does squaring it get rid of more than just one surd?
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  4. #4
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    OH WAIT i see it now....

    X^2 = 2 + X
    X^2 - X - 2 = 0
    (X-2)(X+1) = 0

    so X = 2 or X = -1

    so it must equal 2 because it can't be negative

    =D thanks
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