# $L=\mathbb{Q}(\alpha,\beta)$ such that $\alpha^3 + \alpha + 1 = 0$ and $\beta^2 + \beta -3 = 0$. Find $[L:\mathbb{Q}]$

Let $L=\mathbb{Q}(\alpha,\beta)$ such that $\alpha^3 + \alpha + 1 = 0$ and $\beta^2 + \beta -3 = 0$. Find $[L:\mathbb{Q}]$.