If $\mathbb Q[a,b]$ is a field, then are $a$ and $b$ algebraic?

Question

I have some difficulties in solving the following problem:

If $\mathbb{Q}[\alpha, \beta]$ is a field, then are $\alpha, \beta$ algebraic over $\mathbb{Q}$?

It is likely to be true in my thought, but I have some difficulties in proving. Can anybody help me..?