Algebra question
Hard · from the problemset algebra collection
02
$$x^2-2x+3=0 \text{ has roots } \alpha\:,\beta.\\
\text{Let } \displaystyle \alpha^3-3\alpha^{2}+5\alpha-2 =\phi\text{ and }
\beta^{3}-\beta^2+\beta+5=\chi \\
\text{ Then find } \left( \phi+\chi \right)+\left( \phi\chi \right)$$
