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

Explanation

`alpha*beta=4`

`alpha+beta=2`

`alpha^2+beta^2=(alpha+beta)^2-2alphabeta`

`=4-8=-4`

`(a+b)^3=a^3+b^3+3ab(a+b)`

`(alpha^2+beta^2)^3=alpha^6+beta^6+3alpha^2beta^2(alpha^2+beta^2)`

`-64=alpha^6+beta^6+3*16(-4)`

`alpha^6+beta^6=192-64=128`

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