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    How do I solve c_n+2=c_n(a+b^2) where a and b are constants.
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    I take it a and b are constant (or at least independent of n)?

    in which case, let c_n = \lambda^n and solve for \lambda. You'll get two non-zero roots \lambda = \alpha, \beta, so then c_n = a \alpha^n + b\beta^n, and so on... all the standard method.
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    (Original post by nuodai)
    I take it a and b are constant (or at least independent of n)?

    in which case, let c_n = \lambda^n and solve for \lambda. You'll get two non-zero roots \lambda = \alpha, \beta, so then c_n = a \alpha^n + b\beta^n, and so on... all the standard method.

    So I get \lambda^{n+2}-\lambda^n(a+b^2)=0

    But I can't see how to solve this :P
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    (Original post by Jooeee)
    So I get \lambda^{n+2}-\lambda^n(a+b^2)=0

    But I can't see how to solve this :P
    Factorise it. Hint: look for a common factor.
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    (Original post by nuodai)
    Factorise it. Hint: look for a common factor.
     \lambda^n(\lambda^2-(a+b^2)=0

    So  \lambda^2=(a+b^2)

    so  \lambda=\pm\sqrt(a+b^2)
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    (Original post by Jooeee)
     \lambda^n(\lambda^2-(a+b^2)=0

    So  \lambda^2=(a+b^2)

    so  \lambda=\pm\sqrt(a+b^2)
    Yarp.
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    (Original post by nuodai)
    Yarp.
    Ok thanks, I had got this solution before. So then my general solution would be

     C_n=\alpha\sqrt(a+b^2)+\beta\sqr  t(a+b^2)

    But it says to show that the general solution is

     C_n=\alpha(a+b)^n+\beta(a-b)^n

    But I can't see where this comes from at all.
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    (Original post by Jooeee)
    Ok thanks, I had got this solution before. So then my general solution would be

     C_n=\alpha\sqrt(a+b^2)+\beta\sqr  t(a+b^2)
    It would actually be c_n = \alpha (\sqrt{a+b^2})^n + \beta (-\sqrt{a+b^2})^n.

    (Original post by Jooeee)
    But it says to show that the general solution is

     C_n=\alpha(a+b)^n+\beta(a-b)^n

    But I can't see where this comes from at all.
    I would expect that would be the solution to c_{n+2} - 2ac_{n+1} + c_n(a^2-b^2) = 0, which definitely isn't what you said. Are you sure you copied out the question correctly? If not, it's probably a typo somewhere in the question.
 
 
 
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