Let $K$ be a field of characteristic $0$. Let $C/K$ be a be a quasi-projective conic defined over $K$. Let $L/K$ be a finite dimensional field extension of **odd** dimension. Assume that
$C(L)$ is not empty. 


**Q**: Then is true that $C(K)$ is not empty? If so, then how does one prove it?



On rational points of conics
You can find an elementary proof in
[Un théorème arithmétique sur les coniques](https://doi.org/10.1007/BF02590881 "zbMATH review at https://zbmath.org/0048.02702") by Trygve Nagell in Ark. f. Mat. 2 (1952). This is
a quadratic analogue of what Birch called Heegner's Lemma, which deals with the solvability of certain quartic equations.


