[tex]Avem~de~comparat~ \frac{19}{20} ~si~ \frac{20}{21} . \\ \\ 19 \cdot 21=(20-1)(20+1)=20^2-1^2=20^2-1. \\ \\ 20 \cdot 20 =20^2. \\ \\ Deoarece~20^2-1\ \textless \ 20^2,~rezulta ~\frac{19}{20}\ \textless \ \frac{20}{21} \Leftrightarrow \boxed{a\ \textless \ b}~. [/tex]
