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Mixing bracket types when writing solutions?

  1. Sep 17, 2012 #1

    trollcast

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    Is it okay to mix the types of brackets you use when writing out a solution to help make it a bit clearer?

    For example:

    If I was completeing the square with:

    $$ 3x^{2} + 5x -2 = 0 $$

    I would factor out the 3 onto square brackets like this:

    [itex]3 \left[x^{2} + \frac{5}{3}x - \frac{2}{3} \right] = 0 [/itex]

    Then do my competing the square with round brackets:

    $$ 3 \left[ \left( x + \frac{5}{6} \right)^{2} -\left(\frac{5}{6}\right)^{2} - \frac{2}{3} \right] = 0 $$
     
    Last edited: Sep 17, 2012
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  3. Sep 17, 2012 #2

    micromass

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    Yes, that is perfectly ok. It is even recommended.

    Also, I think you made some calculations errors when completing the square.
     
  4. Sep 17, 2012 #3

    trollcast

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    Thanks,

    There probably are errors as I was about ready to punch my tv trying to get latex to put in the brackets, turns out I had spelled right as rigt.

    Edit: I think fixed the mistake.
     
  5. Sep 17, 2012 #4

    mfb

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    In your example, I would divide both sides by 3, then you do not need the big brackets at all.
    If that is not possible, [ ] are fine.
     
  6. Sep 17, 2012 #5

    trollcast

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    In some questions they ask for the answer in the form, $$ a(x - b)^{2} + c $$

    But yeah if I was just solving to find x I'd divide through, I probably have a few better examples here of where you could use multiple brackets but that was what came to mind first.
     
  7. Sep 17, 2012 #6

    dextercioby

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    If the question is indeed about 'bracketing' and not about completing the square, then I can only say that what you're doing is not right in my book, brackets 'evolve', as the expression gets more complicated. First you place a round bracket, then if you need to put a round bracket into the first round bracket, the initial round brackets become square. If furthermore, you need a new round bracket into the newly created round bracket, the square one will become a brace, the previously existing round bracket will become square. And more, well, the number of braces will increase, since we don't have new types anymore.
     
  8. Sep 17, 2012 #7

    Mark44

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    Maybe it's a British English vs. American English thing, but as I learned them, there are
    • brackets - [] (AKA "square brackets", which IMO is redundant, since brackets already are square)
    • braces - {} (AKA "curly" brackets)
    • parentheses - () (AKA "round" brackets)
     
  9. Sep 17, 2012 #8

    dextercioby

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    Apparently Dirac called these things <> brackets, else he would not have coined the words bra for <| and ket for |>. :biggrin:
     
  10. Sep 17, 2012 #9

    Mark44

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    They're also called angle brackets. They're not normally used for grouping mathematical expressions, I don't believe.
     
  11. Sep 17, 2012 #10
    Not to mention those things that hold your trousers up.
     
  12. Sep 17, 2012 #11

    Mark44

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    Belts? :tongue:
     
  13. Sep 17, 2012 #12
  14. Sep 18, 2012 #13

    NascentOxygen

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    Can also embrace the use of different sized parenthesis pairs, e.g.,

    23((4x + 5) - x(x + 1))
     
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