<s>[INST] 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 $(a-2)(b-2)(c-2)$
 [/INST] You know that: $$a+b+c=3$$ $$ab+bc+ac=0$$ $$abc=-1$$
Also, $$(a-2)(b-2)(c-2)=abc-2(ab+bc+ac)+4(a+b+c)-8$$

So $$(a-2)(b-2)(c-2)=-1-2(0)+4(3)-8=3$$

For cubic with roots as $$\frac a{a-2},\frac b{b-2},\frac c{c-2}$$
Find out $$\frac a {a-2}+\frac b{b-2}+\frac c{c-2}$$
and $$\frac a{a-2}\cdot \frac b{b-2} + \frac b{b-2}\cdot \frac c{c-2} + \frac a{a-2}\cdot \frac c{c-2}$$ by taking LCM and rigorous solving.  
You already know that $$\frac a{a-2}\cdot \frac b{b-2} \cdot \frac c{c-2}=3$$
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