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Math Help - Square roots.

  1. #1
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    Square roots.



    x^2=4
    x=+/-2
    x^2=y
    x=sqrt(y) or +/-sqrt(y)

    what is the ans and why?
    Last edited by mr fantastic; September 4th 2010 at 02:35 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by stupidguy View Post


    x^2=4
    x=+/-2
    x^2=y
    x=sqrt y or +/-sqrt y

    what is the ans and why?
    (In \mathbb{R})

    \sqrt{y} is defined nonnegative. In other words, \sqrt{4} = 2, not \pm 2.

    Thus x^2=y\iff x=\pm \sqrt{y}
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  3. #3
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    x^2=4y, x=?
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    Quote Originally Posted by stupidguy View Post
    x^2=4y, x=?
    Same thing.

    x=\pm \sqrt{4y}=\pm2\sqrt{y}
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    Member grgrsanjay's Avatar
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    x=\pm \sqrt{4y}=\pm2\sqrt{y}
    if
    x = \sqrt{4y^2} then
     x  = +2y
    Last edited by grgrsanjay; September 5th 2010 at 05:55 AM.
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    Quote Originally Posted by grgrsanjay View Post
    x=\pm \sqrt{4y}=\pm2\sqrt{y}
    if
    x = \sqrt{4y} then
     x  = +2y
    you are confusing me!! wat u mean?
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    Member grgrsanjay's Avatar
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    Quote Originally Posted by grgrsanjay View Post
    x=\pm \sqrt{4y}=\pm2\sqrt{y} this is solution for your actual question
    if
    x = \sqrt{4y^2} then if this is your question
     x  = +2y
    .
    Last edited by grgrsanjay; September 5th 2010 at 05:53 AM.
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  8. #8
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by grgrsanjay View Post
    x = \sqrt{4y} then
     x  = +2y
    I also don't know what you mean. The statement

    " x = \sqrt{4y} \implies x = 2y"

    is only true if y = 1.
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  9. #9
    Member grgrsanjay's Avatar
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    i mean y^2 sorry
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  10. #10
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    Quote Originally Posted by grgrsanjay View Post
    i mean y^2 sorry
    But the statement

    " x = \sqrt{4y^2} \implies x = 2y"

    is still not generally true. It should be

    x = \sqrt{4y^2} \implies x = 2|y|
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  11. #11
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    Quote Originally Posted by undefined View Post
    But the statement

    " x = \sqrt{4y^2} \implies x = 2y"

    is still not generally true. It should be

    x = \sqrt{4y^2} \implies x = 2|y|
    Why?
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  12. #12
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by stupidguy View Post
    Why?
    Think about when y is negative.
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  13. #13
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by stupidguy View Post
    Why?
    because  \sqrt{x^2}= |x| is by the definition
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  14. #14
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    if y is negative so be it.
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  15. #15
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    Quote Originally Posted by yeKciM View Post
    because  \sqrt{x^2}= |x| is by the definition
    Are you sure? Can someone verify? the absolute sign seems superfluous.
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