9.1. Which of the numbers is greater: $\sqrt{100^{2}-99}+\sqrt{99^{2}-100}$ or $\sqrt{100^{2}-100}+\sqrt{99^{2}-99}$ ?
Answer: the second number is greater. Solution. Let $a=100, b=99, A=\sqrt{a^{2}-b}+\sqrt{b^{2}-a}$, $B=\sqrt{a^{2}-a}+\sqrt{b^{2}-b}$. We have equivalent inequalities (after squaring and eliminating like terms) $A>0$ (since $\left.a \neq b\right)$.