1.
Let α\alpha and β\beta be the roots of the equation x2+x+1=0x^2 + x + 1 = 0. Then for y0y \neq 0 in R\mathbb{R}, y+1αβαy+β1β1y+α\begin{vmatrix} y+1 & \alpha & \beta \\ \alpha & y+\beta & 1 \\ \beta & 1 & y+\alpha \end{vmatrix} is equal to: