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Math Help - Basic algebra help

  1. #1
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    Basic algebra help

    Hello,

    I have a small algebra problem that i hope anyone can help me with. I have this example in my textbook that have this step i don't follow.

    y_n-y_(n-1)-2y_(n-2) = 0 where n = 3,4,5,...

    y_1 = 1
    y_2 = 3

    with y_n = x^n

    x^n-x^(n-1)-2x^(n-2)=0

    And what i don't understand is how they get this that to this:
    x^2-x-2=0
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  2. #2
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    Re: Basic algebra help

    Quote Originally Posted by mariusg View Post
    Hello,

    I have a small algebra problem that i hope anyone can help me with. I have this example in my textbook that have this step i don't follow.

    y_n-y_(n-1)-2y_(n-2) = 0 where n = 3,4,5,...

    y_1 = 1
    y_2 = 3

    with y_n = x^n

    x^n-x^(n-1)-2x^(n-2)=0

    And what i don't understand is how they get this that to this:
    x^2-x-2=0
    divide every term by xn-2 ...
    Thanks from mariusg
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  3. #3
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    Re: Basic algebra help

    Quote Originally Posted by mariusg View Post
    x^n-x^(n-1)-2x^(n-2)=0
    And what i don't understand is how they get this that to this:
    x^2-x-2=0
    HINT:
    \frac{x^n}{x^{n-2}}=x^2
    Thanks from mariusg
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  4. #4
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    Re: Basic algebra help

    yn - yn-1 2 yn-2 = 0
    yn-2+2 - yn-2+1 2 yn-2 = 0
    yn-2 y2 - yn-2 y 2 yn-2 = 0
    Now divide the equation by yn-2 and we get
    Yn-2 ( y2 - y 2 ) = 0 and that gives y2 - y 2 = 0
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  5. #5
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    Re: Basic algebra help

    Thank you all, i had a little hand to the head moment when i discovered it. (so i took a break from math for the rest of the day)
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