If $\alpha+\beta=1$ and $\alpha^2+\beta^2=2$ then $\alpha^4+\beta^4=$

Question

Professor PC Thomas Classes · Answer

$ \begin{aligned} & 2 \alpha \beta=(\alpha+\beta)^2-\left(\alpha^2+\beta^2ight)=1-2=-1 \ & \alpha \beta=\frac{-1}{2} \ & \alpha^4+\beta^4=\left(\alpha^2+\beta^2ight)^2-2 \alpha^2 \beta^2 \end{aligned} $