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How is this possible?

  1. Jan 19, 2008 #1
    [tex] \sqrt{e^{2t}+2+e^{-2t}} = e^t+e^{-t} [/tex]

    I just can't see it.
     
  2. jcsd
  3. Jan 19, 2008 #2
    The square root of expression A is expression B. So, what is the square of expression B?
     
  4. Jan 19, 2008 #3
    [tex]\sqrt{e^{2t}+2+\frac{1}{e^{2t}}}[/tex]

    Simplify it, then put it in the sum of a product form.
     
  5. Jan 19, 2008 #4
    [tex] (e^t+e^{-t})^2 = e^{2t}+2+e^{-2t} [/tex]

    Not 100% sure but is e^t+e^-t = 1 ?
     
  6. Jan 19, 2008 #5
    No but ... this is equal to 1

    [tex]\frac{e^t}{e^t}=1[/tex]
     
  7. Jan 19, 2008 #6
    sorry I meant e^t * e^-t = 1

    because e^t * 1/e^t = 1....
     
  8. Jan 19, 2008 #7

    arildno

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    No it is not, don't mix * with +!
     
  9. Jan 19, 2008 #8
    I know this is a stupid question, but is there a website that shows what the letters after the exponents stand for?
     
  10. Jan 19, 2008 #9
    I'm not sure what you're asking :(
     
  11. Jan 19, 2008 #10

    HallsofIvy

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    Is there a webset that shows what the letter "x" stands for? You can let letters stand for whatever you want. Perhaps it would make sense if gave an example to show exactly what you mean.
     
  12. Jan 19, 2008 #11
    like [Tex] e^{2t} [/Tex] what would the t stand for?
     
  13. Jan 19, 2008 #12
    [tex]e^t[/tex] ???

    t can be any number, it could even be [tex]x^2[/tex]

    [tex]e^3[/tex]

    or

    [tex]e^{x^2}[/tex]

    In general, the letters at the beginning of the alphabet are denoted for constants such as numbers 1, 2, 3 ... etc. while the letters at the end of the alphabet ... x, y, z are used for variables ... an unknown number that we're looking for.
     
    Last edited: Jan 19, 2008
  14. Jan 20, 2008 #13
    Ahh ok. Thank you very much. I thought it meant specific numbers!
     
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