Complex root of equation 1 let $a,b$ & $c$ are the roots of cubic $$x^3-3x^2+1=0$$
Find a cubic whose roots are $\frac a{a-2},\frac b{b-2}$  and $\frac c{c-2} $
hence or otherwise find value of $(a-2)(b-2)(c-2)$

HINT
We have that $(x-a)(x-b)(x-c)=x^3-3x^2+1$ and then


*

*$a+b+c=3$

*$ab+bc+ca=0$

*$abc=-1$
