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Thread: sqrt (a^2 + b^2) = a + b

  1. #1
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    sqrt (a^2 + b^2) = a + b

    What are all the a,b values that make this expression true expression:
    sqrt(a^2 + b^2) = a + b

    ?
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  2. #2
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    Re: sqrt (a^2 + b^2) = a + b

    $\sqrt{a^2 + b^2} = a+b$

    $a^2 + b^2 = a^2 + 2ab + b^2$

    $0=2ab$

    so either $a=0$, or $b=0$, or both.
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    Re: sqrt (a^2 + b^2) = a + b

    Quote Originally Posted by romsek View Post
    $\sqrt{a^2 + b^2} = a+b$
    $a^2 + b^2 = a^2 + 2ab + b^2$
    $0=2ab$
    so either $a=0$, or $b=0$, or both.
    Here is a counter-example.
    Suppose $a=0~\&~b=-2$ then $\sqrt{0^2+(-2)^2}\ne 0+(-2)=-2$
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    Re: sqrt (a^2 + b^2) = a + b

    Quote Originally Posted by Plato View Post
    Here is a counter-example.
    Suppose $a=0~\&~b=-2$ then $\sqrt{0^2+(-2)^2}\ne 0+(-2)=-2$
    virtually anyone else on the forum would have simply replied

    "you need to include $a,b \geq 0$"

    but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.
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    Re: sqrt (a^2 + b^2) = a + b

    Quote Originally Posted by romsek View Post
    virtually anyone else on the forum would have simply replied
    "you need to include $a,b \geq 0$" but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.
    virtually??? In understand not everyone thinks like a mathematician.

    P.S. as an after-thought. Given the history of the original poster, I very much was addressing him/her.
    Last edited by Plato; Sep 6th 2018 at 10:34 AM.
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    Re: sqrt (a^2 + b^2) = a + b

    Quote Originally Posted by romsek View Post
    > > > virtually anyone else < < < on the forum would have simply replied

    "you need to include $a,b \geq 0$"
    You're presumptuous. I'm fluent in elementary to intermediate algebra, and I missed what Plato pointed out (for the moment).



    but not you. No you have to provide a "counter-example" to show I'm wrong w/o actually helping the original poster any. Well done Plato, well done.
    This was simply an opportunity for you to post to Plato instead "Thank you, I did not clarify and/or emphasize that point you made for the student,
    together with what I already showed."
    Last edited by greg1313; Sep 6th 2018 at 10:42 AM.
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  7. #7
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    Re: sqrt (a^2 + b^2) = a + b

    Another solution:
    Can I suppose a,b be complex numbers?
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