About a year ago (I think around October or November last year) there were a series of questions whose solution strategy set up a polynomial and used its roots to find the solution. I really liked these solution strategies and I'm now trying to remember the specifics.
I only have a vague recollection of the questions but one of the questions went something like: if $1+1/a=x$ and $1+1/a^2=y$ then what is $1+1/a^3$? The solution started by defining a polynomial $P(t)=t^3-(y+y+z)t^2+ t+2(xy+xz+yz)t+xyz$ where $x$ and $y$ and $z=1+1/a^3$ are roots of this polynomial.
Can anyone help?