<s>[INST] If $x^3-9x^2+21x-3=0$ then evaluate $x(3-x)^2$ If $x^3-9x^2+21x-3=0$ then evaluate $x(3-x)^2$.
I managed to write the equation as  $(x-3)^3-6(x-3)+6=0$ but could not proceed further.
 [/INST] By brute force, you find that the only real solution to 
$ x^3-9x^2+21x-3=0 $ 
is $x = 3-2^{1/3}-2^{2/3}$ and hence 
$$
x(3-x)^2 = 3 (2-2^{2/3})
$$
However, I wonder what is the deeper meaning behind this question?
</s>