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Finding the perfect square

  1. Mar 10, 2012 #1
    how do you find the perfect square of say

    ax2 + b/x2 + c
    ??
     
  2. jcsd
  3. Mar 10, 2012 #2

    Mentallic

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    You can't find the perfect square of that problem precisely, unless you're satisfied with [tex]\left(\sqrt{ax^2+\frac{b}{x^2}+c}\right)^2[/tex] which I doubt since it's trivial, but take a look at the expansion of

    [tex]\left(x+\frac{1}{x}\right)^2[/tex]
     
  4. Mar 11, 2012 #3

    Mark44

    Staff: Mentor

    You didn't by chance mean (ax2 + b)/(x2 + c), did you? If so, the lack of parentheses around the numerator and denominator completely confused Mentallic about what you're asking.
     
  5. Mar 11, 2012 #4

    Mentallic

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    That possibility completely skipped my mind :biggrin:
     
  6. Mar 11, 2012 #5

    Mark44

    Staff: Mentor

    Mentallic,
    Well, I'm about as puzzled by this problem as you must be. The way I read it, the OP just wants to square the original expression, whatever it is.
     
  7. Mar 11, 2012 #6
    Nope that is what I ment to say.. I added an example to the paint doc and highlighted the portion in red.

    It has to do with finding the surface area of a curve... and basically I was unaware the equation could be turned into a perfect square... so was wondering if there is some pattern I should look for ?
     

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  8. Mar 11, 2012 #7

    Mentallic

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    I didn't have any doubts about what the OP is trying to do, just what the expression was meant to be once you raised the point.


    Mike, like I was saying it doesn't work in general that ax2 + b/x2 + c can be turned into a perfect square, but in this case c happened to be the right number for the job.

    When you get to the expression

    [tex]\frac{25}{36}x^8+\frac{1}{2}+\frac{9}{100}x^{-8}[/tex]

    You should realize that it could be of the form [tex]\left(ax^4+bx^{-4}\right)^2[/tex] where in this case [tex]a=\sqrt{\frac{25}{36}}=\frac{5}{6}[/tex]
    [tex]b=\sqrt{\frac{9}{100}}=\frac{3}{10}[/tex]

    And all you'd need to do is check to see if [tex]2\cdot \frac{5}{6}\cdot \frac{3}{10} =\frac{1}{2}[/tex]
     
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