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Equation cant solve

  1. Jul 11, 2008 #1
    how do i solve this equatio?
    [(√2) +1]²¹=[(√2)-1]*[3+2(√2)]˟ˉ¹


    (√2) is sqare root of 2

    hhow do i find x?

    how can i divide [(√2) +1]²¹ by =[(√2)-1]
     
  2. jcsd
  3. Jul 11, 2008 #2

    Borek

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    Staff: Mentor

    I don't see x in your equation.
     
  4. Jul 11, 2008 #3
    theres your x Borek.
     
  5. Jul 11, 2008 #4

    Borek

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    Perhaps I am missing something, or it is just my computer glitch, but I have no idea where and what the unknown is and I can't see it with this formatting neither in Opera nor in IE. I see either some square or nothing on the right - but even after checking its code (#735) I am not wiser, as by name that's "swedish grave accent"...

    Is it shaped as x? Is this the equation?

    [tex](\sqrt 2 + 1) ^{21} = \frac {(\sqrt 2 - 1)(3+2 \sqrt 2)} {x}[/tex]
     
  6. Jul 11, 2008 #5
    I'm confused as well. It appears that the x is located as an exponent of [3 + 2*sqrt(2)], more like:

    [3 + 2*sqrt(2)]^(x-1)
     
    Last edited: Jul 11, 2008
  7. Jul 11, 2008 #6

    Borek

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    Something like

    [tex](\sqrt 2 + 1) ^{21} = (\sqrt 2 - 1)(3+2 \sqrt 2) ^{x-1}[/tex]
     
  8. Jul 11, 2008 #7
    Yeah like that.

    Sorry about what I posted earlier, I changed it since I accidently put -x instead of x-1 :smile:
     
  9. Jul 11, 2008 #8
    exactly that, x-1 is the exponent
     
  10. Jul 11, 2008 #9

    HallsofIvy

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    So your problem is simply to solve a= bcx-1 where a, b, c are numbers?

    Surely you see that cx-1= (a/b). Now take the logarithm of both sides.
     
  11. Jul 12, 2008 #10

    gel

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    First , you can write
    [tex]
    \frac{1}{\sqrt{2}-1}=\frac{\sqrt{2}+1}{(\sqrt{2}+1)(\sqrt{2}-1)}=\sqrt{2}+1.
    [/tex]
    Also,
    [tex]
    (\sqrt{2}+1)^2=2+2\sqrt{2}+1=3+2\sqrt{2}.
    [/tex]
    Hopefully, that helps
     
  12. Jul 12, 2008 #11

    arildno

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    Dearly Missed

    Your equation is of the form:
    [tex]a=b*c^{x-1}[/tex]
    where a,b,c are ugly numbers.
    Solve for x in this GENERAL form first, and then, if you absolutely have to, substitute them with your ugly numbers.
     
  13. Jul 12, 2008 #12

    gel

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    I disagree totally with this. The general answer would be x=log(a/b)/log(c)+1, but the point of the original question seems to be to do some simple arithmetic in [tex]Z[\sqrt{2}][/itex], and the answer is an integer, and can be solved exactly without resorting to log tables or a calculator. Expressed as logs, that would not be clear.
     
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