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Math Help - 3x = Square root of 3 + x

  1. #1
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    3x = Square root of 3 + x

    Can someone please let me know if i done this correctly?
    And if there is a faster way I'd love to know.
    3x = \sqrt{3+x}

    3x^2 = (3+x)^2

    3x^2 = 3^2 + x^2

     3x^2 - x^2 = 3^2

    2x^2 = 3^2

     \frac{2x^2}{2} = \frac{9}{2}

     x^2 = 4.5

     x = 2.121
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by el123 View Post
    Can someone please let me know if i done this correctly?...
    No, you have not.

    Your second step is wrong. It should be

    (3x)^2=(\sqrt{3+x})^2

    9x^2=3+x

    S0me of your remaining steps are questionable as well.
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  3. #3
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    (Psst, this should have been posted in the Pre-Algebra/Algebra subforum.)

    Quote Originally Posted by el123 View Post
    Can someone please let me know if i done this correctly?
    And if there is a faster way I'd love to know.
    3x = \sqrt{3+x}

    {\color{red}3x^2 = (3+x)^2}
    Oops! That's not how to do it. You have to square both sides this way:

    (3x)^2 = (\sqrt{3+x})^2

    On the left side, both the 3 and x get squared. On the right side, the square-root and the power of 2 "cancel-out":

    9x^2 = 3 + x

    9x^2 - x - 3 = 0

    Then use the quadratic formula to solve for x.


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    EDIT: Beaten to it...
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  4. #4
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    Quote Originally Posted by el123 View Post
    3x = \sqrt{3+x}
    3x^2 = (3+x)^2
    Hmmm....do you have a math teacher? Or are you self-learning?

    The question is asked for this reason:
    it is easier to help someone if I know whether the person asking for help
    is a classroom student or someone learning on his/her own.
    Last edited by mr fantastic; August 1st 2009 at 04:58 AM. Reason: Added the motive for the question that was subsequently posted by Wilmer
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  5. #5
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    Quote Originally Posted by el123 View Post
     x^2 = 4.5

     x = 2.121
    Even though others have pointed out an earlier mistake you made, I just want to let you know that there's a problem with this step, also. When taking the square root of both sides of an equation, you need to use the plus-or-minus sign, unless the question specifically tells you the answer is positive. Hence

    x^2=4.5 \implies x\approx\pm 2.121.

    Of course, as I and others have said, this is still not the correct value of x for your problem; I just wanted to point out another place you went wrong in the hope of being helpful.
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  6. #6
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    Quote Originally Posted by el123 View Post
    3x^2 = (3+x)^2\;\;\;\; (2)

    3x^2 = 3^2 + x^2\;\;\;\; (3)
    Also, ignoring the fact that you arrived at step 2 incorrectly, when going from step 2 to step 3, you need to FOIL.
    (3 + x)^2 \neq 3^2 + x^2

    (3 + x)^2 = 3^2 + 3x + 3x + x^2 = 9 + 6x + x^2

    For the love of (insert deity here), please remember this next time. I can't tell you how many times I've seen people make the same mistake. It's a pet peeve of mine. Arrrrgh!


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  7. #7
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    Thanks for the help. Was a mistake , i should've seen what i had done wrong. Haven't done math in such a long time. Sometimes i just can't see where i've gone wrong. Hence why i asked for help.
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  8. #8
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    Hi el123

    That's ok. This is indeed where you can seek for help ^^
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