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Non-trivial equation

  1. Jan 25, 2005 #1
    1)write root(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself

    2)suppose m,n(m,n is natural numbers) are such that m/n=root(3),use (1) to write root(3)as another combination of m and n.
    3)use (2) to show that root(3) in not rational.

    Any hints appreciated..
     
  2. jcsd
  3. Jan 26, 2005 #2

    Tide

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    How about

    [tex]\sqrt 3 - 1 = \frac {2}{1+\sqrt 3}[/tex]?
     
  4. Jan 26, 2005 #3

    HallsofIvy

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    Which, I think, would then give [itex]x- 1= \frac{2}{x+1}[/itex] as a non-trivial equation for [itex]\sqrt{3}[/itex].

    If [itex]\frac{m}{n}= \sqrt{3}[/itex], then [itex]\frac{m}{n}-1= \frac{2}{\frac{m}{n}+1}[/itex]. Does that lead to anything?
     
  5. Jan 26, 2005 #4
    Hmm. How do you define non-trivial?
     
  6. Jan 26, 2005 #5
    thanx a lot!

    thanks a lot to all you guys!
    really appreciated..



     
  7. Jan 27, 2005 #6

    HallsofIvy

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    I would consider anything other than [itex]x= \sqrt{3}[/itex] to be "non-trivial"!
     
  8. Jan 27, 2005 #7
    Another question

    root(3)=(m+3n)/(m+n), if m,n is allowed having the common factor,Does it lead to any contradiction?
     
  9. Feb 8, 2005 #8
    i was wondering wut the answer would be for question 3) for general knowledge
     
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