If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$ then the value of $\alpha^6+\beta^6$ is 
If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$ then the value
  of $\alpha^6+\beta^6$ is

I know that, here, $\alpha\beta=4$ and $\alpha + \beta = 2$ and use that result to find $\alpha^2 + \beta^2$ using the expansion of $(a+b)^2$
But how to find $\alpha^6+\beta^6$ ?

Use this one:
$$[(a+b)^2-2ab)][((a+b)^2-2ab)^2-3a^2b^2]$$
