anonymous
  • anonymous
ack - radicals in the denominator: simplify (-L * sqrt (5/2)) / (1- sqrt (5/2))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{ -L \sqrt{5/2} }{1-\sqrt{5/2} }\]
anonymous
  • anonymous
wolfram says the answer is \[\frac{ 1 }{ 3 }L(5-\sqrt{10}) \] and no idea how it gets there from here
zepdrix
  • zepdrix
\[\Large \frac{-L\sqrt{\frac{5}{2}}}{1-\sqrt{\frac{5}{2}}}\] Mmmm this one is a tad tricky due to all the fractions. I would recommend first multiplying through by 2/2. Err actually let's multiply through by \(\large \sqrt2/\sqrt2\). Ya ya ya, I think that will work out nicely.

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zepdrix
  • zepdrix
\[\Large \frac{-L\sqrt5}{\sqrt2-\sqrt5}\]Understand that step?
anonymous
  • anonymous
ok because sqrt 5/2 is also sqrt 5/sqrt 2
zepdrix
  • zepdrix
true story :D
anonymous
  • anonymous
then can multiply by sqrt 2 - sqrt 5
zepdrix
  • zepdrix
Mmm close! :) We want to multiply by the `conjugate` of our denominator. \[\Large \frac{-L\sqrt5}{\sqrt2-\sqrt5}\color{royalblue}{\left(\frac{\sqrt2+\sqrt5}{\sqrt2+\sqrt5}\right)}\]
anonymous
  • anonymous
that conjugate trick always seems like cheating to me
zepdrix
  • zepdrix
why's that? :x
anonymous
  • anonymous
sure go ahead and just change signs all willynilly any other time and see how far you get =)
zepdrix
  • zepdrix
I mean, the only sneaky thing we're doing is multiplying by 1 in a strange way.\[\Large \color{royalblue}{\left(\frac{\sqrt2+\sqrt5}{\sqrt2+\sqrt5}\right)} \quad=\quad 1\]
zepdrix
  • zepdrix
The reason we multiply by the conjugate is because it produces the `difference of squares` when you multiply out all the terms.\[\Large (a-b)(a+b)=a^2-b^2\] And that gets rid of the roots for us.
anonymous
  • anonymous
I agree that it works...it is just....not an obvious move and therefore sneaky so that gets a negative 3 in the denominator and (-L)(sqrt 5) (sqrt 2 + sqrt5) on top negative L and negative 3 explains Wolfram's 1/3
zepdrix
  • zepdrix
Once you get into the math groove, it becomes a rather obvious move :\ But maybe that's just my experience.. :p
anonymous
  • anonymous
distribute the sqrt 5 gets (sqrt 5 * sqrt 2) = sqrt 10 and sqrt 5 * sqrt 5 is 5 and look the answer pops right out
zepdrix
  • zepdrix
Speaking of which, it's NOT a move you have to make. You could instead just do the subtraction in the denominator instead of fussing with the conjugate multiplication. It's just a little trickier to do it that way.
anonymous
  • anonymous
my mileage will vary... well thanks a ton hated leaving the answer half done especially since I knew I'd set it up right one medal for you
zepdrix
  • zepdrix
:3

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