I don't know how to do this question:

Given that alpha is a root of the equation x^2=2x-3 show that alpha^3=alpha-6.

I have a list of equations involving the roots calling them alpha and beta.

2. Hello Stuck Man
Originally Posted by Stuck Man
I don't know how to do this question:

Given that alpha is a root of the equation x^2=2x-3 show that alpha^3=alpha-6.

I have a list of equations involving the roots calling them alpha and beta.
If $\displaystyle \alpha$ is a root, then:
$\displaystyle \alpha^2=2\alpha-3$ (1)
Multiply both sides by $\displaystyle \alpha$:
$\displaystyle \Rightarrow \alpha^3 = (2\alpha-3)\alpha$
$\displaystyle =2\alpha^2-3\alpha$

$\displaystyle = 2(2\alpha -3)-3\alpha$, using (1)
I'm sure you can complete it now.

3. I see, thanks.

Is there any particular topic that results such as this are in?:
a^2+b^2=(a+b)^2-2ab

4. Hello Stuck Man
Originally Posted by Stuck Man
I see, thanks.

Is there any particular topic that results such as this are in?:
a^2+b^2=(a+b)^2-2ab
Not really. It's part of general algebraic manipulation, which will turn up in all sorts of situations - in particular, the solution of polynomial equations, factorisation, etc.