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.

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- Jan 3rd 2010, 06:40 AMStuck ManQuadratics question
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. - Jan 3rd 2010, 06:57 AMGrandad
Hello Stuck ManIf $\displaystyle \alpha$ is a root, then:

$\displaystyle \alpha^2=2\alpha-3$ (1)Multiply both sides by $\displaystyle \alpha$:

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

$\displaystyle = 2(2\alpha -3)-3\alpha$, using (1)

Grandad - Jan 3rd 2010, 07:12 AMStuck Man
I see, thanks.

Is there any particular topic that results such as this are in?:

a^2+b^2=(a+b)^2-2ab - Jan 3rd 2010, 07:26 AMGrandad