In the previous problem's post ((2) Evaluate The Sum Of 1/xy+z-1+1/yz+x-1+1/xz+y-1 ), we said if we let $k=\dfrac{1}{\dfrac{4}{x}+x-1}$, we will then have $k^3+\dfrac{2}{9}k^2-\dfrac{2}{81}k-\dfrac{4}{81}= 0$.
In this post, we will reveal the logic and reason behind it and guide you step-by-step in achieving the other cubic polynomial where $k^3+\dfrac{2}{9}k^2-\dfrac{2}{81}k-\dfrac{4}{81}= 0$.