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Can't get this

  1. Aug 2, 2005 #1
    can't get this!!!

    Hi there,
    I have a question that I cannot solve. Here it is.

    [tex]\frac{1}{\sqrt(4-2\sqrt3)}=x+y\sqrt3 [/tex]

    then what is x^2+y^2?

    All I did was finding what left hand side stood for. It equals

    [tex]\frac{\sqrt3 + 1}{2} [/tex]

    Any help?
  2. jcsd
  3. Aug 2, 2005 #2


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    if i understand u right then tht implies x=y=1/2......so find wht u want...
  4. Aug 2, 2005 #3
    How does he implies that? I got there before but I supposed that x and y are not irrational
  5. Aug 2, 2005 #4
    do you know the numerical solution for this problem ?

  6. Aug 2, 2005 #5
    hello ? are you dead ?
  7. Aug 2, 2005 #6


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    Staff Emeritus
    Science Advisor

    If x and y are rational, then x= y= 1/2 so x2+ y2= 1/2 is the only solution. If x and y are allowed to be rational, then there are an infinite number of solutions.
  8. Aug 2, 2005 #7
    how is the left hand side equal to [tex]\frac{\sqrt3 + 1}{2} [/tex] ?

  9. Aug 2, 2005 #8
    that's because of this.

    suppose that a=x+y and b=xy then

    [tex]\sqrt (a + 2\sqrt b) = \sqrt x+ \sqrt y [/tex]

    Ivy, I don't get what you mean. How do you know if the numbers x and y are rational then the only solution is x=y=0.5? and how do you know there is an infinite number of solutions if they are irrational?
  10. Aug 3, 2005 #9


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    if x and y are rational then irrational terms on both sides of the eq must be equal adn also rational terms on both sides must be equal.hence y=x=0.5....get it?
  11. Aug 3, 2005 #10
    yeah I know it, I said I did it that way. But the problem is that nothing is told about it. Anyway thnaks, I think the question wasn't complete in this case
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