Mixing bracket types when writing solutions?

  • Thread starter trollcast
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  • #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:

$$ 3 \left[ \left( x + \frac{5}{6} \right)^{2} -\left(\frac{5}{6}\right)^{2} - \frac{2}{3} \right] = 0 $$
 
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Answers and Replies

  • #2
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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.
 
  • #3
trollcast
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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.

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.
 
  • #4
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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.
 
  • #5
trollcast
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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.

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.
 
  • #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.
 
  • #7
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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)
 
  • #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:
 
  • #9
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They're also called angle brackets. They're not normally used for grouping mathematical expressions, I don't believe.
 
  • #10
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Not to mention those things that hold your trousers up.
 
  • #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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