1.2.1. (2 points) Let $x_{1}$ and $x_{2}$ be the roots of the equation $\sqrt{14} x^{2}-\sqrt{116} x+\sqrt{56}=0$. Calculate $\left|\frac{1}{x_{1}^{2}}-\frac{1}{x_{2}^{2}}\right|$. Answer: $\frac{\sqrt{29}}{14} \approx 0.38$.
Solution. For the equation $a x^{2}+b x+c=0$ we have

$$
\left|\frac{1}{x_{1}^{2}}-\frac{1}{x_{2}^{2}}\right|=\frac{\left|x_{2}-x_{1}\right| \cdot\left|x_{2}+x_{1}\right|}{x_{1}^{2} \cdot x_{2}^{2}}=\frac{\left|\frac{\sqrt{D}}{a}\right| \cdot\left|\frac{-b}{a}\right|}{\frac{c^{2}}{a^{2}}}=\frac{|b| \sqrt{D}}{c^{2}}
$$