anonymous
  • anonymous
r^6 - 3r^4 + 3r^2 - 1 = 0 .. How to solve this differential equation ???
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Factorise it if you want. Though it may be easier to let x = r^2 than factorise that (it's a standard expansion if you recognise it; if not you can find a factor (or three) by inspection). Then \[r = \pm \sqrt{x} \]
anonymous
  • anonymous
ohh yea i get it! thanks alot !
myininaya
  • myininaya
does this help r=1 multplicity 3 r=-1 multplicity 3
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anonymous
  • anonymous
:) If you're interesting, it actually factorises it it's original for as: \[(r-1)^3(r+1)^3 \] Which I think is quite quaint.
myininaya
  • myininaya
i tried to factor don't look at that first part where i factor r^4 of the first two terms
myininaya
  • myininaya
i got lucky and synthetic division worked since all r all are rational zeros
anonymous
  • anonymous
@myininaya. thanks it sure did help
anonymous
  • anonymous
@newton. but u will have to factorise to get that answer, no ? we cant figure it out directly, can we ?
anonymous
  • anonymous
\[(r-1)^3(r+1)^3 = 0 \iff r = \pm 1 \]
anonymous
  • anonymous
yes yes i get it. what i meant to say was that we will have to factorise the original expression using division to reach to this answer ?
anonymous
  • anonymous
Not necessarily using division, you could compare coefficients of something.
anonymous
  • anonymous
(after spotting a few factors by inspection - in this case they are so obvious, but normally trying -2, -1, 1, 2 will get at least one)
myininaya
  • myininaya
look i have something else if you didnt like synthetic
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myininaya
  • myininaya
=(r^2-1)^3
anonymous
  • anonymous
:D thanks alot. i get it
myininaya
  • myininaya
thats alot of work for one problem lol
anonymous
  • anonymous
haha yea that sure is. im highly obliged
myininaya
  • myininaya
so none of the algebra I did needs explaining?
anonymous
  • anonymous
nope its quite clear :) i completely get it, thanks to you :)
myininaya
  • myininaya
:)
anonymous
  • anonymous
@myininaya. could you please repost your cal0009.pdf attachment. it won't open for me. thanks

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