[tex]\displaystyle\bf\\\frac{a}{3}=\frac{2}{b}=\frac{c}{5}=k;~~~k \in N\\\\a=3k\\\\b=\frac{2}{k}\\\\c=5k\\\\\text{\bf Dam valori lui }~k\\\\\boxed{\bf k=1}\\\\a=3k=3\times1=3\\\\b=\frac{2}{k}=\frac{2}{1}=2\\\\c=5k=5\times1=5\\\\\boxed{\bf k=2}\\\\a=3k=3\times2=6\\\\b=\frac{2}{k}=\frac{2}{2}=1\\\\c=5k=5\times2=10\\\\\text{Pentru }~k=3~\text{ rezulta }~~b=\frac{2}{k}=\frac{2}{3}\notin N\\ \\\text{Rezulta ca avem doar 2 solutii:}\\\\S_1\to~a=3;~b=2;~c=5\\S_1\to~a=6;~b=1;~c=10[/tex]
