find x Watch

drmath
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#1
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#1
if

x=1+ω^x+ω^{2x}

find x

ω is The cube root of unity
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generalebriety
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Is x real or complex?
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drmath
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x real
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ViolatedTreason
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#4
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(Original post by drmath)
if

x=1+ω^x+ω^{2x}

find x

ω is The cube root of unity
x is here,here and here x=1+ω^x+ω^{2x}
duh... lol

[/sarcasm]

ill give anyone rep who can figure this out.. cos it amazes me how people can calculate stuff like this...
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generalebriety
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Well, x = 3 is an "obvious" solution.
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generalebriety
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Further to this, I think basic algebra has us solving sin(2x.pi/3) = 0 or cos(2x.pi/3) = -1/2, and we can verify easily that none of the other potential solutions (0, 1, -1, 3/2, -3/2, 2, -2) work.
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SimonM
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When I equate imaginary parts to zero, I am left with sin \pi x = 0 rather than sin 2/3 \pi x or cos \pi /3 x =0
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Cities
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3 isn't it :confused:
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drmath
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x-1= ω^x+ω^{2x}

(x-1)^2=(ω^x+ω^{2x})^2

x^2-2x+1=ω^{2x}+2ω^{3x}+ω^{4x}

but
ω^{4x}=ω,ω^{3x}=1,x-1=ω^x+ω^{2x}


x^2-3x=0

x=0(not work), x=3

thank you
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highachiever
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does anyone know any A2 level chemistry CD rom online to buy?

i will appreciate if anyone replies

thx...
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pyrolol
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(Original post by highachiever)
does anyone know any A2 level chemistry CD rom online to buy?

i will appreciate if anyone replies

thx...
Don't spam. Nobody is going to reply to you if you post it all over the place in the wrong forums. You will however get lots of neg rep, and maybe worse. Try making a single post (preferably a bit more informative...you're not exactly clear what you want), in the right forum (that means: not here!).
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Cities
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(Original post by drmath)
x-1= ω^x+ω^{2x}

(x-1)^2=(ω^x+ω^{2x})^2

x^2-2x+1=ω^{2x}+2ω^{3x}+ω^{4x}

but
ω^{4x}=ω,ω^{3x}=1,x-1=ω^x+ω^{2x}


x^2-3x=0

x=0(not work), x=3

thank you
Neat method. Is there any way of doing it without squaring it (and creating unwanted values of x?)

I must admit, you come across as a tad scary lol.
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quintsy
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#13
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(Original post by highachiever)
does anyone know any A2 level chemistry CD rom online to buy?

i will appreciate if anyone replies

thx...
Please start a new thread if you have a question- you're far more likely to get relevant responses that way than if you post in existing, unrelated threads. This has been mentioned to you before, and if you continue with it you will be warned.
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