Abstract
The Manin conjecture is established for Châtelet surfaces over $\mathbf{Q}$ arising as minimal proper smooth models of the surface $Y^2+Z^2=f(X)$ in $\mathbf{A}_{\mathbf{Q}}^3$, where $f\in \mathbf{Z}[X]$ is a totally reducible polynomial of degree $3$ without repeated roots. These surfaces do not satisfy weak approximation.
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