Exercise 1, § 3

Let E be an extension of a field K and x and y two distinct roots in E of the same irreducible polynomial of $K[X]$. Show that the extensions $K(x)$ and $K(y)$ are not linearly disjoint over K (use Th. 2). \* Give an example where $K = \mathbf{Q}$ and $K(x) \cap K(y) = K$ (cf. V, p. 161, Ex. 2).