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.
Grandad