2. A line passes through the point with coordinates $(10 ; 0)$ and intersects the parabola $y=$ $x^{2}$ at points with abscissas $x_{1}$ and $x_{2}$. Find $\frac{1}{x_{1}}+\frac{1}{x_{2}}$.
Answer: 0.1.

Solution. The points $\mathrm{x}_{1}, \mathrm{x}_{2}$, are solutions to the equation $x^{2}=k(x-10)$, where $\mathrm{k}$ is the slope coefficient of the line. Then, by Vieta's theorem, $x_{1}+x_{2}=k, x_{1} x_{2}=10 k$. Therefore, $\frac{1}{x_{1}}+\frac{1}{x_{2}}=\frac{x_{1}+x_{2}}{x_{1} x_{2}}=\frac{k}{10 k}=\frac{1}{10}$.