9.1. Solve the equation $\left|x^{2}-100\right|=2 x+1$.
Answer. $x_{1}=1+\sqrt{102}, x_{2}=9$. Solution. If $x^{2}-100 \geq 0$, i.e., under the condition $|x| \geq 10$, we have the equation $x^{2}-2 x-101=0$, its roots are $x=1 \pm \sqrt{102}$. The root $1+\sqrt{102}$ satisfies the condition $|x| \geq 10$, while the root $1-\sqrt{102}$ does not. If $|x|<10$, then we have the equation $x^{2}+2 x-99=0$, its roots are $x=-1 \pm 10$, and the condition $|x|<10$ is only satisfied by the root $x=9$.