[tex]\boxed{\bold{1.}}~ \\ 13x+11=11x+13 \\ 13x-11x=13-11 \\ 2x=2 \Rightarrow \boxed{x=1}. \\ \\ \boxed{ \bold{2.}} \\ a \in \{0,1,8 \} \\ b \in \{1,4,9 \} \\ \\ Daca~a=0,~atunci~ \frac{a}{1}= \frac{a}{4}= \frac{a}{9}=0.~aceste~3~fractii~se~numara~ca~ \\ una~singura. \\ \\ Deci~exista~3 \cdot 3-2=7~fractiI~cu~proprietatea~din~enunt. [/tex]
[tex] \boxed{ \bold{3.}}\\ \\ \overline{ab}\ \textless \ \overline{ba} \\ 10a+b\ \textless \ 10b+a \\ 10a-a\ \textless \ 10b-b \\ 9a\ \textless \ 9b \\ a\ \textless \ b \\ \\ \\ Evident:~a,b \neq 0. \\ a=1 \Rightarrow b \in \{2,3,4,...,9 \} \\ a=2 \Rightarrow b\in \{3,4,5,...,9\} \\ ........................................ \\ a=8 \Rightarrow b=9 [/tex]
[tex]Sa~observam~ca~daca~a=k,~unde~k \in \{1,2,3,...,8\},~atunci~b \\ poate~avea~9-k~valori. \\ \\ Deci~in~total~exista: \\ \\ (9-1)+(9-2)+(9-3)+...+(9-8)= \\ =8+7+6+...+1= \\ = \frac{8 \cdot 9}{2}= \\ =36~astfel~de~fractii. [/tex]
