Posers and Puzzles

Posers and Puzzles

  1. Hendersonville, NC
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    27 Aug '03 19:58
    I guess one could probably find this somewhere on the internet; but, can anyone tell me why this is incorrect:

    -20=-20
    16-36=-20
    25-45=-20
    16-36=25-45
    16-36+(81/4)=25-45+(81/4)
    (4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
    4-(9/2)=5-(9/2)
    4=5
    1=2 (subtracting 3 from each side)
  2. Donationrichjohnson
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    27 Aug '03 20:14
    Originally posted by Cheshire Cat
    I guess one could probably find this somewhere on the internet; but, can anyone tell me why this is incorrect:

    -20=-20
    16-36=-20
    25-45=-20
    16-36=25-45
    16-36+(81/4)=25-45+(81/4)
    (4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
    4-(9/2)=5-(9/2)
    4=5
    1=2 (subtracting 3 from each side)
    You are taking the negative root of the expression on the left and the positive root of the expression on the right.

    Another example:
    (-2)^2 = 4
    (2)^2 = 4
    (-2)^2 = (2)^2
    -2 = 2
  3. Hendersonville, NC
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    27 Aug '03 20:171 edit
    Originally posted by richjohnson
    You are taking the negative root of the expression on the left and the positive root of the expression on the right.

    Another example:
    (-2)^2 = 4
    (2)^2 = 4
    (-2)^2 = (2)^2
    -2 = 2
    I see. Does that mean that the correct answer would be something like 2i=2?
  4. Standard memberroyalchicken
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    27 Aug '03 20:371 edit
    No.

    (-2)^2 = 2^2=4

    All this is an indication of is the fact that every positive real number has two real square roots.

    (2i)^2 = -4
  5. Hendersonville, NC
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    27 Aug '03 20:45
    Originally posted by royalchicken
    No.

    (-2)^2 = 2^2=4

    All this is an indication of is the fact that every positive real number has two real square roots.

    (2i)^2 = -4
    Right....does that also apply to the first equation?
  6. Standard memberroyalchicken
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    27 Aug '03 21:01
    (4-(9/2))^2=(-0.5)^2

    (5-(9/2))^2=(0.5)^2

    As richjohnson said, you can't make the negative and positive roots equivalent.
  7. Hendersonville, NC
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    27 Aug '03 21:14
    Originally posted by royalchicken
    (4-(9/2))^2=(-0.5)^2

    (5-(9/2))^2=(0.5)^2

    As richjohnson said, you can't make the negative and positive roots equivalent.
    Hmmm. I'll have to look at that one some more. How about this one:

    x=.999999999....repeating 9s
    10x=9.999999....repeating 9s

    Using systems I think:

    ~~~~10x=9.999....~~~
    ~~~~~-x=.9999....~~~
    ---------------------------

    ~~~~~9x=9~~~~~~~~

    x=1
    x=.99999....

    1=.999999......

    Hope that is understandable.
  8. Standard memberroyalchicken
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    27 Aug '03 21:16
    Originally posted by Cheshire Cat
    Hmmm. I'll have to look at that one some more. How about this one:

    x=.999999999....repeating 9s
    10x=9.999999....repeating 9s

    Using systems I think:

    ~~~~10x=9.999....~~~
    ~~~~~-x=.9999....~~~
    ---------------------------

    ~~~~~9x=9~~~~~~~~

    x=1
    x=.99999....

    1=.999999......

    Hope that is understandable.
    That's fine, since 1 = 0.9 rec. There's another thread on this in this forum. Good job, though.
  9. Hendersonville, NC
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    27 Aug '03 21:21
    Originally posted by royalchicken
    That's fine, since 1 = 0.9 rec. There's another thread on this in this forum. Good job, though.
    Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
  10. Donationrichjohnson
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    27 Aug '03 21:27
    Originally posted by Cheshire Cat
    Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
    They are actually the same number (rec = "recurring&quot😉.

    Incidentally, the series S=(1/2 + 1/4 + 1/8 + 1/16 + ...) is also equal to one.

    Why?

    2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...)

    2S-S=1
  11. Standard memberroyalchicken
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    27 Aug '03 21:30
    Originally posted by Cheshire Cat
    Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
    Yeah, sorry. 09. rec is shorthand for 0.999999999999999999...........
  12. Hendersonville, NC
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    27 Aug '03 21:35
    Originally posted by richjohnson
    They are actually the same number (rec = "recurring"😉.

    Incidentally, the series S=(1/2 + 1/4 + 1/8 + 1/16 + ...) is also equal to one.

    Why?

    2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...)

    2S-S=1
    That's all well and good, but the question is why do they work.
  13. my own little world
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    28 Aug '03 01:161 edit
    -20=-20
    16-36=-20
    25-45=-20
    16-36=25-45
    16-36+(81/4)=25-45+(81/4)
    (4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
    4-(9/2)=5-(9/2)
    4=5
    1=2 (subtracting 3 from each side)


    the first problem works due, as RichJohnson said, because all positive real numbers have two roots both the negative and the positive. Therefore, if you take 2^2 and -2^2 you will get 4 for both. The reason this works is because the eqaution, although, mathematically correct is not balanced correctly. (Or, atleast thats what my maths teacher would say as I messed up a question, in a paper, because I did just this and got the wrong answer🙂)

    Hmmm. I'll have to look at that one some more. How about this one:

    x=.999999999....repeating 9s
    10x=9.999999....repeating 9s

    Using systems I think:

    ~~~~10x=9.999....~~~
    ~~~~~-x=.9999....~~~
    ---------------------------

    ~~~~~9x=9~~~~~~~~

    x=1
    x=.99999....

    1=.999999......

    Hope that is understandable.


    the second was explained to me but I can't for the life of me remember. I'll ask some people and see if they can tell me.
  14. Hendersonville, NC
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    28 Aug '03 01:31
    Originally posted by jimmi t
    [b]-20=-20
    16-36=-20
    25-45=-20
    16-36=25-45
    16-36+(81/4)=25-45+(81/4)
    (4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
    4-(9/2)=5-(9/2)
    4=5
    1=2 (subtracting 3 from each side)


    the first problem works due, as RichJohnson said, because all positive real numbers have two roots both the negative and the positive. Therefore, if you take 2^2 and -2 ...[text shortened]... me but I can't for the life of me remember. I'll ask some people and see if they can tell me.[/b]
    Cool, thanks.
  15. Standard memberFiathahel
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    28 Aug '03 09:19
    One canalso think asfollows

    1/9 = 0.11111111111111111111...
    2/9 = 0.22222222222222222222...
    3/9 = 0.333333333333333333...
    :
    :
    9/9 = 0.999999999999999999...
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