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Thread: Factoring Trouble

  1. #1
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    Question Factoring Trouble

    All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
    Perhaps there's no solution. IDK.

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    Quote Originally Posted by hgraff View Post
    All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
    Perhaps there's no solution. IDK.
    There is no such number

    [tex]2x = 60 \implies \frac{1}{2} * 2x = \frac{1}{2} * 60 \implies x = 30 \implies x^2 = 900 \ne 890.[/tex]

  3. #3
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    Base -3/2

    Quote Originally Posted by hgraff View Post
    All I need to know is what number, when squared, equals 890, and when doubled, equals 60. No, it's not 30. Any ideas?
    Perhaps there's no solution. IDK.
    Yes it is 30,
    if all numbers are base -3/2
    "What happens in the event horizon, stays in the event horizon" -- Bob Brown (grandpa Bob)

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    Hello, Bob Brown!

    Very imaginative!
    I got a different answer.


    Quote Originally Posted by Bob Brown MSEE View Post
    Yes it is 30, if all numbers are base -3/2

    Let [tex]b[/tex] = base, [tex]bx+y[/tex] = two-digit number.

    We have: .[tex]\begin{Bmatrix}(bx+y)^2 \;=\; 8b^2+9b & [1] \\ 2(bx+y) \;=\; 6b & [2] \end{Bmatrix}[/tex]

    From [2]: .[tex]y \:=\:3b-bx[/tex]

    Substitute into [1]: .[tex][bx + (3b-bx)]^2 \:=\:8b^2 + 9b[/tex]

    . . . [tex](3b)^2 \:=\:8b^2+9b \quad\Rightarrow\quad 9b^2 \:=\:8b^2 + 9b[/tex]

    . . . [tex]b^2 - 9b \:=\:0 \quad\Rightarrow\quad b(b-9) \:=\:0[/tex]

    . . . [tex]\color{red}{\rlap{/////}}{b = 0},\;b = 9[/tex]


    We are dealing with base-nine.
    . . And it turns out that [tex]x = 3,\;y = 0.[/tex]


    Check:

    . . [tex]\begin{Bmatrix}(30_9)^2 \;=\;8\color{purple}{9}0_9 & \Rightarrow & 27^2 \:=\:729 & \checkmark \\ 2(30_9) \;=\;60_9 & \Rightarrow & 2(27) \:=\:54 & \checkmark \end{Bmatrix}[/tex]


    Unfortunately, there is no "9" in base-nine . . . *sigh*

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    So it is just possible that Bob Brown was right all along?

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    Hmmmmmmmm

    Quote Originally Posted by HallsofIvy View Post
    So it is just possible that Bob Brown was right all along?
    possible
    "What happens in the event horizon, stays in the event horizon" -- Bob Brown (grandpa Bob)

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    Quote Originally Posted by Bob Brown MSEE View Post
    possible
    Instead of "possible," it is definite.


    http://en.wikipedia.org/wiki/Negative_base



    State it with conviction.

    As a tangential example,

    one would state with conviction that [tex]2x^2 - x + 3 < 0 [/tex]

    (or similar expression) would not be presented as, say,

    2xx - x + 3 < 0.


    --------------------------------------------



    Edit: "Definitively missing the joke."

    Or I "got the joke" and deliberately was dismissive of it.
    Last edited by lookagain; 02-20-2013 at 05:42 PM.

  8. #8
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    Quote Originally Posted by lookagain View Post
    Instead of "possible," it is definite.
    Definitively missing the joke.

    Question

    Quote Originally Posted by HallsofIvy
    So it is just possible that Bob Brown was right all along?
    Answer

    Quote Originally Posted by Bob Brown MSEE
    possible

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