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Math Help - Need some help please

  1. #1
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    Need some help please

    I've got a question I'm really not sure how to do. here it is:

    Consider the following difference equation:
    q(n) = 2*q(n-1) + q(n-2) - 2*q(n-3)

    Let q(n) = ar^n. Show that r must satisfy (r-1)(r+1)(r-2) = 0

    It doesnt look to hard, im just not quiet sure exactly how to go about it...
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  2. #2
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    Quote Originally Posted by mrtwigx View Post
    I've got a question I'm really not sure how to do. here it is:

    Consider the following difference equation:
    q(n) = 2*q(n-1) + q(n-2) - 2*q(n-3)

    Let q(n) = ar^n. Show that r must satisfy (r-1)(r+1)(r-2) = 0

    It doesnt look to hard, im just not quiet sure exactly how to go about it...
    Substitute the trial solution into the difference equation:

    ar^n = 2 a r^{n-1} + a r^{n-2} - 2a r^{n-3}.

    Simplify and re-arrange:

    \Rightarrow r^{n-3} \left( r^3 - 2r^2 - r + 2\right) = 0.

    Since r \neq 0 you're left with r^3 - 2r^2 - r + 2 = 0.
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  3. #3
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    Thanks for your reply, it realy was helpfull. I feel a little stupid that I couldnt get it myself...
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