1. 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

2. Re: Basic algebra help

Originally Posted by mariusg
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 ...

3. Re: Basic algebra help

Originally Posted by mariusg
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:
$\frac{x^n}{x^{n-2}}=x^2$

4. 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

5. 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)